###### Advertisements

###### Advertisements

If sin 3θ = cos (θ – 6°) where 3θ and θ − 6° are acute angles, find the value of θ.

###### Advertisements

#### Solution

3θ, θ – 6 are an acute angle

We know that sin (90 – θ) = cos θ

sin 3θ = sin (90 – (θ - 6°))

sin 3θ = sin(90 – θ + 6°)

sin 3θ = sin (96° - θ)

3θ = 96° – θ

4θ = 96°

`θ = 96^@/4`

`θ = 24^@`

#### APPEARS IN

#### RELATED QUESTIONS

if `sec A = 5/4` verify that `(3 sin A - 4 sin^3 A)/(4 cos^3 A - 3 cos A) = (3 tan A - tan^3 A)/(1- 3 tan^2 A)`

In rectangle ABCD AB = 20cm ∠BAC = 60° BC, calculate side BC and diagonals AC and BD.

In right angled triangle ΔABC at B, ∠A = ∠C. Find the values of Sin A cos C + Cos A Sin C

If sin θ = cos (θ – 45°), where θ – 45° are acute angles, find the degree measure of θ

If sin θ = ` (a^2 - b^2)/(a^2+b^2)`find all the values of all T-ratios of θ .

If 3tan θ 4 , show that `((4cos theta - sin theta ))/((4 cos theta + sin theta))=4/5`

If A = 45^{0 }, verify that:

(ii) cos 2A = 2 cos^{2} A – 1 = 1 – 2 sin^{2} A

If A = 30^{0 }, verify that:

(ii) cos 2A = `(1- tan^2A)/(1+tan^2A)`

If A = 60^{0} and B = 30^{0}, verify that:

(ii) cos (A – B) = cos A cos B + sin A sin B

Using the formula, cos A = `sqrt((1+cos2A)/2) ,`find the value of cos 30^{0}, it being given that cos 60^{0} = `1/2`.

In the following table, a ratio is given in each column. Find the remaining two ratios in the column and complete the table.

sin θ |
`11/61` | `1/2` | `3/5` | ||||||

cos θ |
`35/37` | `1/sqrt3` | |||||||

tan θ |
`1` | `21/20` | `8/15` | `1/(2sqrt2)` |

`(cos 28°)/(sin 62°)` = ?

sin20°^{ } = cos ______°

tan 30° × tan ______° = 1

cos 40° = sin ______°

Form the following figure, find the values of:

- cos B
- tan C
- sin
^{2}B + cos^{2}B - sin B. cos C + cos B. sin C

In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ∠ABC.

In the figure given below, ABC is an isosceles triangle with BC = 8 cm and AB = AC = 5 cm. **Find:**

(i) sin B

(ii) tan C

(iii) sin^{2} B + cos^{2}B

(iv) tan C - cot B

In the given figure;

BC = 15 cm and sin B = `(4)/(5)`

- Calculate the measure of AB and AC.
- Now, if tan ∠ADC = 1; calculate the measures of CD and AD.

Also, show that: tan^{2}B - `1/cos^2 "B" = – 1 .`

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

tanB = `(8)/(15)`

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

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

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

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

From the given figure, find the values of sin B

From the given figure, find the values of sec B

From the given figure, find the values of cos C

From the given figure, find the values of tan C

If cos A = `(2x)/(1 + x^2)`, then find the values of sin A and tan A in terms of x

If sin θ = `"a"/sqrt("a"^2 + "b"^2)`, then show that b sin θ = a cos θ

If 3 cot A = 2, then find the value of `(4sin"A" - 3cos"A")/(2sin"A" + 3cos"A")`

If cos θ : sin θ = 1 : 2, then find the value of `(8costheta - 2sintheta)/(4costheta + 2sintheta`

A boy standing at a point O finds his kite flying at a point P with distance OP = 25 m. It is at a height of 5 m from the ground. When the thread is extended by 10 m from P, it reaches a point Q. What will be the height QN of the kite from the ground? (use trigonometric ratios)

Given that sin α = `1/2` and cos β = `1/2`, then the value of α + β is ______.