Chapters
Chapter 2: Compound Interest (Without using formula)
Chapter 3: Compound Interest (Using Formula)
Chapter 4: Expansions (Including Substitution)
Chapter 5: Factorisation
Chapter 6: Simultaneous (Linear) Equations (Including Problems)
Chapter 7: Indices (Exponents)
Chapter 8: Logarithms
Chapter 9: Triangles [Congruency in Triangles]
Chapter 10: Isosceles Triangles
Chapter 11: Inequalities
Chapter 12: Mid-point and Its Converse [ Including Intercept Theorem]
Chapter 13: Pythagoras Theorem [Proof and Simple Applications with Converse]
Chapter 14: Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Chapter 15: Construction of Polygons (Using ruler and compass only)
Chapter 16: Area Theorems [Proof and Use]
Chapter 17: Circle
Chapter 18: Statistics
Chapter 19: Mean and Median (For Ungrouped Data Only)
Chapter 20: Area and Perimeter of Plane Figures
Chapter 21: Solids [Surface Area and Volume of 3-D Solids]
Chapter 22: Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and their Reciprocals]
Chapter 23: Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter 24: Solution of Right Triangles [Simple 2-D Problems Involving One Right-angled Triangle]
Chapter 25: Complementary Angles
Chapter 26: Co-ordinate Geometry
Chapter 27: Graphical Solution (Solution of Simultaneous Linear Equations, Graphically)
Chapter 28: Distance Formula

Chapter 23: Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Selina solutions for Concise Mathematics Class 9 ICSE Chapter 23 Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] Exercise 23 (A) [Pages 291 - 292]
find the value of: sin 30° cos 30°
find the value of: tan 30° tan 60°
find the value of: cos2 60° + sin2 30°
find the value of: cosec2 60° - tan2 30°
find the value of: sin2 30° + cos2 30°+ cot2 45°
find the value of: cos2 60° + sec2 30° + tan2 45°
find the value of :
tan2 30° + tan2 45° + tan2 60°
find the value of :
`( tan 45°)/ (cos ec30°) +( sec60°)/(co 45°) – (5 sin 90°)/ (2 cos 0°)`
find the value of :
3sin2 30° + 2tan2 60° - 5cos2 45°
Prove that:
sin 60° cos 30° + cos 60° . sin 30° = 1
Prove that:
cos 30° . cos 60° - sin 30° . sin 60° = 0
Prove that:
cosec2 45° - cot2 45° = 1
Prove that:
cos2 30° - sin2 30° = cos 60°
Prove that:
`((tan60° + 1)/(tan 60° – 1))^2 = (1+ cos 30°) /(1– cos 30°) `
Prove that:
3 cosec2 60° - 2 cot2 30° + sec2 45° = 0
prove that:
sin (2 x 30°) = `(2 tan 30°)/(1+tan^2 30°)`
prove that:
cos (2 x 30°) = `(1 – tan^2 30°)/(1+tan^2 30°)`
prove that:
tan (2 x 30°) = `(2 tan 30°)/(1– tan^2 30°)`
ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratios: sin 45°
ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratio: cos 45°
ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratios: tan 45°
Prove that:
sin 60° = 2 sin 30° cos 30°
Prove that:
4 (sin4 30° + cos4 60°) -3 (cos2 45° - sin2 90°) = 2
If sin x = cos x and x is acute, state the value of x
If sec A = cosec A and 0° ∠A ∠90°, state the value of A
If tan θ = cot θ and 0°∠θ ∠90°, state the value of θ
If sin x = cos y; write the relation between x and y, if both the angles x and y are acute.
If sin x = cos y, then x + y = 45° ; write true of false
True
False
secθ . Cot θ= cosecθ ; write true or false
True
False
For any angle θ, state the value of : sin2 θ + cos2 θ
State for any acute angle θ whether sin θ increases or decreases as θ increases
Increases
Decreases
State for any acute angle θ whether cos θ increases or decreases as θ increases.
Increases
Decreases
State for any acute angle θ whether tan θ increases or decreases as θ decreases.
Increases
Decreases
If `sqrt3` = 1.732, find (correct to two decimal place) the value of sin 60o
If `sqrt3` = 1.732, find (correct to two decimal place) the value of `(2)/(tan 30°)`
Evaluate :
`(cos3"A" – 2cos4"A")/(sin3"A" + 2sin4"A")` , when A = 15°
Evaluate :
`(3 sin 3"B" + 2 cos(2"B" + 5°))/(2 cos 3"B" – sin (2"B" – 10°)` ; when "B" = 20°.
Selina solutions for Concise Mathematics Class 9 ICSE Chapter 23 Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] Exercise 23 (B) [Page 293]
Given A = 60° and B = 30°,
prove that : sin (A + B) = sin A cos B + cos A sin B
Given A = 60° and B = 30°,
prove that : cos (A + B) = cos A cos B - sin A sin B
Given A = 60° and B = 30°,
prove that : cos (A - B) = cos A cos B + sin A sin B
Given A = 60° and B = 30°,
prove that : tan (A - B) = `(tan"A" – tan"B")/(1 + tan"A".tan"B")`
If A =30o, then prove that :
sin 2A = 2sin A cos A = `(2 tan"A")/(1 + tan^2"A")`
If A =30o, then prove that :
cos 2A = cos2A - sin2A = `(1 – tan^2"A")/(1+ tan^2"A")`
If A =30o, then prove that :
2 cos2 A - 1 = 1 - 2 sin2A
If A =30o, then prove that :
sin 3A = 3 sin A - 4 sin3A.
If A = B = 45° ,
show that:
sin (A - B) = sin A cos B - cos A sin B
If A = B = 45° ,
show that:
cos (A + B) = cos A cos B - sin A sin B
If A = 30°;
show that:
sin 3 A = 4 sin A sin (60° - A) sin (60° + A)
If A = 30°;
show that:
(sinA - cosA)2 = 1 - sin2A
If A = 30°;
show that:
cos 2A = cos4 A - sin4 A
If A = 30°;
show that:
`(1 – cos 2"A")/(sin 2"A") = tan"A"`
If A = 30°;
show that:
`(1 + sin 2"A" + cos 2"A")/(sin "A" + cos"A") = 2 cos "A"`
If A = 30°;
show that:
4 cos A cos (60° - A). cos (60° + A) = cos 3A
If A = 30°;
show that:
`(cos^3"A" – cos 3"A")/(cos "A") + (sin^3"A" + sin3"A")/(sin"A") = 3`
Selina solutions for Concise Mathematics Class 9 ICSE Chapter 23 Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] Exercise 23 (C) [Pages 297 - 298]
Solve the following equation for A, if 2 sin A = 1
Solve the following equation for A, if 2cos2A = 1
Solve the following equation for A, if sin 3 A = `sqrt3 /2`
Solve the following equation for A, if sec 2A = 2
Solve the following equations for A, if tan A = 1
Solve the following equation for A, if `sqrt3` tan 3 A = 1
Solve the following equation for A, if 2 sin 3 A = 1
Solve the following equation for A, if `sqrt3` cot 2 A = 1
Calculate the value of A, if (sin A - 1) (2 cos A - 1) = 0
Calculate the value of A, if (tan A - 1) (cosec 3A - 1) = 0
Calculate the value of A, if (sec 2A - 1) (cosec 3A - 1) = 0
Calculate the value of A, if cos 3A. (2 sin 2A - 1) = 0
Calculate the value of A, if (cosec 2A - 2) (cot 3A - 1) = 0
If 2 sin x° - 1 = 0 and x is an acute angle;
find :
(i) sin x°
(ii) x°
(iii) cos x and tan x°.
If 4 cos2 x° - 1 = 0 and 0 ∠ x° ∠ 90°,
find:(i) x°
(ii) sin2 x° + cos2 x°
(iii) `(1)/(cos^2xx°) – (tan^2 xx°)`
If 4 sin2 θ - 1= 0 and angle θ is less than 90°, find the value of θ and hence the value of cos2 θ + tan2θ.
If sin 3A = 1 and 0 < A < 90°, find sin A
If sin 3A = 1 and 0 < A < 90°, find cos 2A
If sin 3A = 1 and 0 < A < 90°, find `tan^2A - (1)/(cos^2 "A")`
If 2 cos 2A = `sqrt3` and A is acute,
find:
(i) A
(ii) sin 3A
(iii) sin2 (75° - A) + cos2 (45° +A)
If sin x + cos y = 1 and x = 30°, find the value of y
If 3 tan A - 5 cos B = `sqrt3` and B = 90°, find the value of A
From the given figure,
find:
(i) cos x°
(ii) x°
(iii) `(1)/(tan^2 xx°) – (1)/(sin^2xx°)`
(iv) Use tan xo, to find the value of y.
Use the given figure to find:
(i) tan θ°
(ii) θ°
(iii) sin2θ° - cos2θ°
(iv) Use sin θ° to find the value of x.
Find the magnitude of angle A, if 2 sin A cos A - cos A - 2 sin A + 1 = 0
Find the magnitude of angle A, if tan A - 2 cos A tan A + 2 cos A - 1 = 0
Find the magnitude of angle A, if 2 cos2 A - 3 cos A + 1 = 0
Find the magnitude of angle A, if 2 tan 3A cos 3A - tan 3A + 1 = 2 cos 3A
Solve for x : 2 cos 3x - 1 = 0
Solve for x : cos `(x)/(3) –1` = 0
Solve for x : sin (x + 10°) = `(1)/(2)`
Solve for x : cos (2x - 30°) = 0
Solve for x : 2 cos (3x - 15°) = 1
Solve for x : tan2 (x - 5°) = 3
Solve for x : 3 tan2 (2x - 20°) = 1
Solve for x : cos `(x/(2)+10°) = (sqrt3)/(2)`
Solve for x : sin2 x + sin2 30° = 1
Solve for x : cos2 30° + cos2 x = 1
Solve for x : cos2 30° + sin2 2x = 1
Solve for x : sin2 60° + cos2 (3x- 9°) = 1
If 4 cos2 x = 3 and x is an acute angle;
find the value of :
(i) x
(ii) cos2 x + cot2 x
(iii) cos 3x (iv) sin 2x
In ΔABC, ∠B = 90° , AB = y units, BC = `(sqrt3)` units, AC = 2 units and angle A = x°,
find:
(i) sin x°
(ii) x°
(iii) tan x°
(iv) use cos x° to find the value of y.
If 2 cos (A + B) = 2 sin (A - B) = 1;
find the values of A and B.
Chapter 23: Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]

Selina solutions for Concise Mathematics Class 9 ICSE chapter 23 - Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
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Concepts covered in Concise Mathematics Class 9 ICSE chapter 23 Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] are Trigonometric Equation Problem and Solution, Trigonometric Ratios of Some Special Angles, Trigonometric Ratios of Some Special Angles, Trigonometric Ratios of Some Special Angles.
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