Frank solutions for Mathematics [English] Class 9 ICSE chapter 26 - Trigonometrical Ratios [Latest edition]

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)`

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

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

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

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

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

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

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

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

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

tanB = `(8)/(15)`

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

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

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

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) sin²θ - cot²θ

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: cot²P - cosec²P

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")`

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 cos² C + cosec² 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 : cot²A - cosec²A

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 5cot²θ + sin²θ - 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 tan²θ + cot²θ

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 4sin³θ - 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 `cot θ = (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)`