#### Chapters

Chapter 2: Profit , Loss and Discount

Chapter 3: Compound Interest

Chapter 4: Expansions

Chapter 5: Factorisation

Chapter 6: Changing the subject of a formula

Chapter 7: Linear Equations

Chapter 8: Simultaneous Linear Equations

Chapter 9: Indices

Chapter 10: Logarithms

Chapter 11: Triangles and their congruency

Chapter 12: Isosceles Triangle

Chapter 13: Inequalities in Triangles

Chapter 14: Constructions of Triangles

Chapter 15: Mid-point and Intercept Theorems

Chapter 16: Similarity

Chapter 17: Pythagoras Theorem

Chapter 18: Rectilinear Figures

Chapter 19: Quadrilaterals

Chapter 20: Constructions of Quadrilaterals

Chapter 21: Areas Theorems on Parallelograms

Chapter 22: Statistics

Chapter 23: Graphical Representation of Statistical Data

Chapter 24: Perimeter and Area

Chapter 25: Surface Areas and Volume of Solids

Chapter 26: Trigonometrical Ratios

Chapter 27: Trigonometrical Ratios of Standard Angles

Chapter 28: Coordinate Geometry

## Chapter 26: Trigonometrical Ratios

### Frank solutions for Class 9 Maths ICSE Chapter 26 Trigonometrical Ratios Exercise 26.1

In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.

sinA = `(12)/(13)`

In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.

cosB = `(4)/(5)`

In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.

cotA = `(1)/(11)`

cose C = `(15)/(11)`

tan C = `(5)/(12)`

sinB = `sqrt(3)/(2)`

cos A = `(7)/(25)`

tanB = `(8)/(15)`

sec B = `(15)/(12)`

cosec C = `sqrt(10)`

In ΔABC, ∠A = 90°. If AB = 5 units and AC = 12 units, find: sinB

In ΔABC, ∠A = 90°. If AB = 5 units and AC = 12 units, find: cos C

In ΔABC, ∠A = 90°. If AB = 5 units and AC = 12 units, find: tan B.

In ΔABC, ∠B = 90°. If AB = 12units and BC = 5units, find: sinA

In ΔABC, ∠B = 90°. If AB = 12units and BC = 5units, find: tan A

In ΔABC, ∠B = 90°. If AB = 12units and BC = 5units, find: cos C

In ΔABC, ∠B = 90°. If AB = 12units and BC = 5units, find: cot C

If sinA = `(3)/(5)`, find cosA and tanA.

If cosB = `(1)/(3)` and ∠C = 90°, find sin A, and B and cot A.

If sin θ = `(8)/(17)`, find the other five trigonometric ratios.

If tan = 0.75, find the other trigonometric ratios for A.

If sinA = 0.8, find the other trigonometric ratios for A.

If 8 tanθ = 15, find (i) sinθ, (ii) cotθ, (iii) sin^{2}θ - cot^{2}θ

In the given figure, PQR is a triangle, in which QS ⊥ PR, QS = 3 cm, PS = 4 cm and QR = 12 cm, find the value of: sin P

In the given figure, PQR is a triangle, in which QS ⊥ PR, QS = 3 cm, PS = 4 cm and QR = 12 cm, find the value of: cot^{2}P - cosec^{2}P

In the given figure, PQR is a triangle, in which QS ⊥ PR, QS = 3 cm, PS = 4 cm and QR = 12 cm, find the value of: 4sin^{2}R - `(1)/("tan"^2"P")`

In an isosceles triangle ABC, AB = BC = 6 cm and ∠B = 90°. Find the values of cos C

In an isosceles triangle ABC, AB = BC = 6 cm and ∠B = 90°. Find the values of cosec C

In an isosceles triangle ABC, AB = BC = 6 cm and ∠B = 90°. Find the values of cos^{2} C + cosec^{2} C

In the given figure, AD is the median on BC from A. If AD = 8 cm and BC = 12 cm, find the value of sin x

In the given figure, AD is the median on BC from A. If AD = 8 cm and BC = 12 cm, find the value of cos y

In the given figure, AD is the median on BC from A. If AD = 8 cm and BC = 12 cm, find the value of tan x. cot y

In the given figure, AD is the median on BC from A. If AD = 8 cm and BC = 12 cm, find the value of `(1)/("sin"^2 x) - (1)/("tan"^2 x)`

In a right-angled triangle PQR, ∠PQR = 90°, QS ⊥ PR and tan R =`(5)/(12)`, find the value of sin ∠PQS

In a right-angled triangle PQR, ∠PQR = 90°, QS ⊥ PR and tan R =`(5)/(12)`, find the value of tan ∠SQR

In the given figure, ΔABC is right angled at B.AD divides BC in the ratio 1 : 2. Find

(i) `("tan"∠"BAC")/("tan"∠"BAD")` (ii) `("cot"∠"BAC")/("cot"∠"BAD")`

If sin A = `(7)/(25)`, find the value of : `(2"tanA")/"cot A - sin A"`

If sin A = `(7)/(25)`, find the value of : `"cos A" + (1)/"cot A"`

If sin A = `(7)/(25)`, find the value of : cot^{2}A - cosec^{2}A

If cosec θ = `(29)/(20)`, find the value of: cosec θ - `(1)/("cot" θ)`

If cosec θ = `(29)/(20)`, find the value of: `("sec" θ)/("tan" θ - "cosec" θ)`

In the given figure, AC = 13cm, BC = 12 cm and ∠B = 90°. Without using tables, find the values of: sin A cos A

In the given figure, AC = 13cm, BC = 12 cm and ∠B = 90°. Without using tables, find the values of: `("cos A" - "sin A")/("cos A" + "sin A")`

In tan θ = 1, find the value of 5cot^{2}θ + sin^{2}θ - 1.

In the given figure, ∠Q = 90°, PS is a median om QR from P, and RT divides PQ in the ratio 1 : 2. Find: `("tan" ∠"PSQ")/("tan"∠"PRQ")`

In the given figure, ∠Q = 90°, PS is a median om QR from P, and RT divides PQ in the ratio 1 : 2. Find: `("tan" ∠"TSQ")/("tan"∠"PRQ")`

In the given figure, AD is perpendicular to BC. Find: 5 cos x

In the given figure, AD is perpendicular to BC. Find: 15 tan y

In the given figure, AD is perpendicular to BC. Find: 5 cos x - 12 sin y + tan x

In the given figure, AD is perpendicular to BC. Find:

`(3)/("sin" x) + (4)/("cos" y) - 4 "tan" y`

In a right-angled triangle ABC, ∠B = 90°, BD = 3, DC = 4, and AC = 13. A point D is inside the triangle such as ∠BDC = 90°.

Find the values of 2 tan ∠BAC - sin ∠BCD

In a right-angled triangle ABC, ∠B = 90°, BD = 3, DC = 4, and AC = 13. A point D is inside the triangle such as ∠BDC = 90°.

Find the values of 3 - 2 cos ∠BAC + 3 cot ∠BCD

If 24cosθ = 7 sinθ, find sinθ + cosθ.

If 4 sinθ = 3 cosθ, find tan^{2}θ + cot^{2}θ

If 4 sinθ = 3 cosθ, find `(6sinθ - 2cosθ )/(6sinθ + 2cosθ )`

If 8tanA = 15, find sinA - cosA.

If 3cosθ - 4sinθ = 2cosθ + sinθ, find tanθ.

If 5cosθ = 3, find the value of `(4cosθ - sinθ)/(2cosθ + sinθ)`

If 4sinθ = `sqrt(13)`, find the value of `(4sinθ - 3cosθ)/(2sinθ + 6cosθ)`

If 4sinθ = `sqrt(13)`, find the value of 4sin^{3}θ - 3sinθ

If 5tanθ = 12, find the value of `(2sinθ - 3cosθ)/(4sinθ - 9cosθ)`.

If 35 sec θ = 37, find the value of sin θ - sin θ tan θ.

If cotθ = `(1)/sqrt(3)`, show that `(1 - cos^2θ)/(2 - sin^2θ) = (3)/(5)`

If cosecθ = `1(9)/(20)`, show that `(1 - sinθ + cosθ)/(1 + sinθ + cosθ) = (3)/(7)`

If b tanθ = a, find the values of `(cosθ + sinθ)/(cosθ - sinθ)`.

If a cotθ = b, prove that `("a"sinθ - "b"cosθ)/("a"sinθ + "b"cosθ) = ("a"^2 - "b"^2)/("a"^2 + "b"^2)`

If cotθ = `sqrt(7)`, show that `("cosec"^2θ -sec^2θ)/("cosec"^2θ + sec^2θ) = (3)/(4)`

If 12cosecθ = 13, find the value of `(sin^2θ - cos^2θ) /(2sinθ cosθ) xx (1)/tan^2θ`.

If 12 cotθ = 13, find the value of `(2sinθ cosθ)/(cos^2θ - sin^2θ)`.

If secA = `(5)/(4)`, cerify that `(3sin"A" - 4sin^3"A")/(4cos^3"A" - 3cos"A") = (3tan"A" - tan^3"A")/(1 - 3tan^2"A")`.

If sinθ = `(3)/(4)`, prove that `sqrt(("cosec"^2θ - cot^2θ)/(sec^2θ - 1)) = sqrt(7)/(3)`.

If secA = `(17)/(8)`, verify that `(3 - 4sin^2 "A")/(4 cos^2 "A" - 3)= (3 - tan^2"A")/(1 - 3tan^2"A")`

If 3 tanθ = 4, prove that `sqrt(secθ - "cosec"θ)/(sqrt(secθ - "cosec"θ)) = (1)/sqrt(7)`.

If tan θ = `"m"/"n"`, show that `"m sin θ - n cos θ"/"m sinθ + n cos θ" = ("m"^2 - "n"^2)/("m"^2 + "n"^2)`

## Chapter 26: Trigonometrical Ratios

## Frank solutions for Class 9 Maths ICSE chapter 26 - Trigonometrical Ratios

Frank solutions for Class 9 Maths ICSE chapter 26 (Trigonometrical Ratios) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Class 9 Maths ICSE solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 9 Maths ICSE chapter 26 Trigonometrical Ratios are Concept of Perpendicular, Base, and Hypotenuse in a Right Triangle, Notation of Angles, Trigonometric Ratios and Its Reciprocal, Reciprocal Relations.

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