# Frank solutions for Class 9 Maths ICSE chapter 26 - Trigonometrical Ratios [Latest edition]

## Chapter 26: Trigonometrical Ratios

Exercise 26.1
Exercise 26.1

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

Exercise 26.1 | Q 1.01

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

sinA = (12)/(13)

Exercise 26.1 | Q 1.02

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

cosB = (4)/(5)

Exercise 26.1 | Q 1.03

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

cotA = (1)/(11)

Exercise 26.1 | Q 1.04

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

cose C = (15)/(11)

Exercise 26.1 | Q 1.05

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

tan C = (5)/(12)

Exercise 26.1 | Q 1.06

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

sinB = sqrt(3)/(2)

Exercise 26.1 | Q 1.07

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

cos A = (7)/(25)

Exercise 26.1 | Q 1.08

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

tanB = (8)/(15)

Exercise 26.1 | Q 1.09

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

sec B = (15)/(12)

Exercise 26.1 | Q 1.1

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

cosec C = sqrt(10)

Exercise 26.1 | Q 2.1

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

Exercise 26.1 | Q 2.2

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

Exercise 26.1 | Q 2.3

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

Exercise 26.1 | Q 3.1

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

Exercise 26.1 | Q 3.2

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

Exercise 26.1 | Q 3.3

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

Exercise 26.1 | Q 3.4

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

Exercise 26.1 | Q 4

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

Exercise 26.1 | Q 5

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

Exercise 26.1 | Q 6

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

Exercise 26.1 | Q 7

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

Exercise 26.1 | Q 8

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

Exercise 26.1 | Q 9

If 8 tanθ = 15, find (i) sinθ, (ii) cotθ, (iii) sin2θ - cot2θ

Exercise 26.1 | Q 10.1

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

Exercise 26.1 | Q 10.2

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: cot2P - cosec2P

Exercise 26.1 | Q 10.3

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: 4sin2R - (1)/("tan"^2"P")

Exercise 26.1 | Q 11.1

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

Exercise 26.1 | Q 11.2

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

Exercise 26.1 | Q 11.3

In an isosceles triangle ABC, AB = BC = 6 cm and ∠B = 90°. Find the values of cos2 C + cosec2 C

Exercise 26.1 | Q 12.1

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

Exercise 26.1 | Q 12.2

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

Exercise 26.1 | Q 12.3

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

Exercise 26.1 | Q 12.4

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)

Exercise 26.1 | Q 13.1

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

Exercise 26.1 | Q 13.2

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

Exercise 26.1 | Q 14

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")

Exercise 26.1 | Q 15.1

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

Exercise 26.1 | Q 15.2

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

Exercise 26.1 | Q 15.3

If sin A = (7)/(25), find the value of : cot2A - cosec2A

Exercise 26.1 | Q 16.1

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

Exercise 26.1 | Q 16.2

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

Exercise 26.1 | Q 17.1

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

Exercise 26.1 | Q 17.2

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")

Exercise 26.1 | Q 18

In tan θ = 1, find the value of 5cot2θ + sin2θ - 1.

Exercise 26.1 | Q 19.1

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")

Exercise 26.1 | Q 19.2

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")

Exercise 26.1 | Q 20.1

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

Exercise 26.1 | Q 20.2

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

Exercise 26.1 | Q 20.3

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

Exercise 26.1 | Q 20.4

In the given figure, AD is perpendicular to BC. Find:
(3)/("sin"  x) + (4)/("cos"  y) - 4 "tan"  y

Exercise 26.1 | Q 21.1

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

Exercise 26.1 | Q 21.2

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

Exercise 26.1 | Q 22

If 24cosθ = 7 sinθ, find sinθ + cosθ.

Exercise 26.1 | Q 23.1

If 4 sinθ = 3 cosθ, find tan2θ + cot2θ

Exercise 26.1 | Q 23.2

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

Exercise 26.1 | Q 24

If 8tanA = 15, find sinA - cosA.

Exercise 26.1 | Q 25

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

Exercise 26.1 | Q 26

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

Exercise 26.1 | Q 27.1

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

Exercise 26.1 | Q 27.2

If 4sinθ = sqrt(13), find the value of 4sin3θ - 3sinθ

Exercise 26.1 | Q 28

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

Exercise 26.1 | Q 29

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

Exercise 26.1 | Q 30

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

Exercise 26.1 | Q 31

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

Exercise 26.1 | Q 32

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

Exercise 26.1 | Q 33

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

Exercise 26.1 | Q 34

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

Exercise 26.1 | Q 35

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

Exercise 26.1 | Q 36

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

Exercise 26.1 | Q 37

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").

Exercise 26.1 | Q 38

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

Exercise 26.1 | Q 39

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

Exercise 26.1 | Q 40

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

Exercise 26.1 | Q 41

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)

Exercise 26.1

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

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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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