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Chapters
2: Compound Interest
3: Expansions
4: Factorisation
5: Simultaneous Linear Equations
6: Indices/Exponents
7: Logarithms
8: Triangles
9: Mid-point Theorem
10: Pythagoras Theorem
11: Rectilinear Figures
12: Constructions of Polygons
13: Theorems on Area
14: Circles
15: Statistics
16: Mensuration
▶ 17: Trigonometric Ratios
18: Trigonometric Ratios of Some Standard Angles and Complementary Angles
Chapter 19: Co-ordinate Geometry: An Introduction
![Nootan solutions for मैथमैटिक्स [अंग्रेजी] कक्षा ९ आईसीएसई chapter 17 - Trigonometric Ratios - Shaalaa.com](/images/mathematics-english-class-9-icse_6:f26eb985e8254aa987299226050d7c71.jpg "Nootan solutions for मैथमैटिक्स [अंग्रेजी] कक्षा ९ आईसीएसई chapter 17 - Trigonometric Ratios")
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Solutions for Chapter 17: Trigonometric Ratios
Below listed, you can find solutions for Chapter 17 of CISCE Nootan for मैथमैटिक्स [अंग्रेजी] कक्षा ९ आईसीएसई.
Nootan solutions for मैथमैटिक्स [अंग्रेजी] कक्षा ९ आईसीएसई 17 Trigonometric Ratios Exercise 17A [Pages 359 - 361]
If `sin θ = 1/3`, find the values of other t-ratios.
If `sin θ = 1/sqrt(2)`, find the values of other t-ratios.
If `cos θ = 7/25`, find the values of other t-ratios.
If `tan θ = 8/15`, find the values of other t-ratios.
Given that `tan θ = 5/12` and angle is an acute angle, find sin θ and cos θ.
If `sin θ = 3/5` and θ is an acute angle, find (i) cos θ, (ii) tan θ.
In a right-angled triangle, it is given that A is an acute angle and that tan A = `3/4`. Without using tables, find the value of cos A.
If `sin θ = 6/10`, find without using table, the value of (cos θ + tan θ).
Using the measurements given in the following figure:
- Find the value of sin Φ and tan θ.
- Write an expression for AD in terms of θ.
In the triangle given below figure, calculate tan θ if ∠B = 90°, AB = 20 cm and AC = 40 cm.
ABC is a right-angled triangle, right-angled at B. Given that ∠ACB = θ, side AB = 2 units and side BC = 1 unit, find the value of sin2θ + tan2θ.
In ΔАBC, AB = AC = 15 cm, BC = 18 cm, find cos ∠ABC.
Given: sin θ = `p/q`, find cos θ + sin θ in terms of p and q.
If `tan θ = 4/3`, find without using tables, the value of sin θ + cos θ (both sin θ and cos θ are positive).
In the following figure, ΔABC is right-angled at B, ΔBSC is right-angled at S and ΔBRS is right-angled at R, AB = 18 cm, BC = 7.5 cm, RS = 5 cm, ∠BSR = x° and ∠SAB = y°. Find (i) tan x°, (ii) sin y°, (iii) cos y°.
If `tan θ = p/q`, then prove that `(p sin θ - q cos θ)/(p sin θ + q cos θ) = ((p^2 - q^2)/(p^2 + q^2))`.
If `cot θ = (1)/sqrt(3)`, show that `((1 - cos^2θ)/(2 - sin^2θ)) = (3)/(5)`.
If `sec θ = 13/5`, show that `(2 sin θ - 3 cos θ)/(4 sin θ - 9 cos θ) = 3`.
If 5 tan θ = 4, show that `(5 sin θ - 3 cos θ)/(5 sin θ + 2 cos θ) = 1/6`.
If `cos θ = 12/13`, show that `sin θ (1 - tan θ) = 35/156`.
If `sin θ = 3/5`, evaluate `((cos θ - 1/(tan θ)))/(2 cot θ)`.
If `sec θ = 5/4`, evaluate `(sin θ - 2 cos θ)/(tan θ - cot θ)`.
If `tan θ = 4/3`, show that `sqrt((1 - sin θ)/(1 + sin θ)) = 1/3`.
If `tan θ = 1/sqrt(7)`, show that `("cosec"^2θ - sec^2θ)/("cosec"^2θ + sec^2θ) = 3/4` .
If tan α = 2, evaluate sin α sec α + tan2α – cosec α.
If `sec θ = 5/4`, verify that `(tan θ)/(1 + tan^2θ) = (sin θ)/(sec θ)`.
Given A is acute angle and 13 sin A = 5, evaluate without using tables: `(5 sin A - 2 cos A)/(tan A)`.
If 5 cos A – 12 sin A = 0, evaluate without using tables `(sin A + cos A)/(2 cos A - sin A)`.
If θ is an acute angle and sin θ = cos θ, find the value of 2 tan2 θ + sin2 θ – 1.
If tan θ + cot θ = 2, prove that tan2θ + cot2θ = 2.
If x = a sin θ + b cos θ, y = a cos θ – b sin θ, prove that x2 + y2 = a2 + b2.
Prove that `1/(1 + tan^2 A) + 1/(1 + cot^2 A) = 1`.
Prove that `tan^2 θ - 1/(cos^2 θ) = -1`.
Nootan solutions for मैथमैटिक्स [अंग्रेजी] कक्षा ९ आईसीएसई 17 Trigonometric Ratios Exercise 17B [Pages 361 - 363]
Multiple Choice Questions Choose the correct answer from the given four options in each of the following questions:
If `sin θ = 5/13`, then cot θ is equal to ______.
`5/12`
`12/5`
`12/13`
`13/12`
If `sec θ = 17/8`, then tan θ is equal to ______.
`15/8`
`8/15`
`15/17`
`17/15`
If `tan θ = 3/5`, then cos θ is equal to ______.
`4/3`
`3/4`
`3/sqrt(34)`
`5/sqrt(34)`
`sqrt((1 - sin^2 θ)/(1 - cos^2 θ)` is equal to ______.
tan θ
cot θ
sec θ
cos θ
If `cot θ = b/a`, then sec2θ – tan2θ is equal to ______.
0
1
–1
`b/sqrt(a^2 + b^2)`
If `sin θ = a/b`, then tan θ is equal to ______.
`a/sqrt(b^2 - a^2)`
`b/sqrt(b^2 - a^2)`
`sqrt(b^2 - a^2)/a`
`sqrt(b^2 - a^2)/b`
If sin θ = 2 cos θ, then `(3 sin θ - cos θ)/(3 sin θ + cos θ)` is equal to ______.
0
`1/2`
`2/5`
`5/7`
cos θ . tan θ is equal to ______.
cot θ
sin θ
cosec θ
sec θ
If tan x + cot x = 2, then tan2x + x + cot2x is equal to ______.
0
1
2
4
If cosec θ = `5/3`, then sin2x + cos2x + 1 is equal to ______.
0
`25/9`
2
`9/25`
Valid Statements Questions
In the following questions, two statements (i) and (ii) are given. Choose the valid statement.
(i) In ΔАВС, ∠A = 90° and sin B = `8/17` then cos B = `15/17`.
(ii) If sin θ = `1/3`, then cos θ = `2/3`.
Only (i)
Only (ii)
Both (i) and (ii)
Neither (i) nor (ii)
In the following questions, two statements (i) and (ii) are given. Choose the valid statement.
(i) If `cot θ = a/b`, then `tan θ = b/a`.
(ii) sin θ · cot θ = cos θ.
Only (i)
Only (ii)
Both (i) and (ii)
Neither (i) nor (ii)
In the following questions, two statements (i) and (ii) are given. Choose the valid statement.
(i) If sin θ + cosec θ = 4 then sin2θ + cosec2θ = 16
(ii) `sqrt((1 - cos^2θ)/(1 - sin^2θ)) = cot θ`
Only (i)
Only (ii)
Both (i) and (ii)
Neither (i) nor (ii)
In the following questions, two statements (i) and (ii) are given. Choose the valid statement.
(i) If `tan θ = 3/4`, then `cos θ = 3/5`
(ii) If sin θ = 3 cos θ, then `(sin θ - cos θ)/(sin θ + cos θ) = 1/2`
Only (i)
Only (ii)
Both (i) and (ii)
Neither (i) nor (ii)
Solutions for 17: Trigonometric Ratios
Nootan solutions for मैथमैटिक्स [अंग्रेजी] कक्षा ९ आईसीएसई chapter 17 - Trigonometric Ratios
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