Question

If sin 3theta =cos(theta -6°),then theta=​

Answer 1

Given,

$\sin3 \theta \: = cos( \theta - {6}^{0} )$

$\implies \: cos( {90}^{0} - 3 \theta) = cos( \theta \: - {6}^{0} )$

$\implies \: {90}^{0} - \theta \: = \theta - {6}^{0}$

$\implies \: 2 \: \theta \: = {90}^{0} + {6}^{0}$

$\implies \: 2 \: \theta \: = {96}^{0}$

$\implies \: \theta \: = \frac{96}{2}$

$\implies \: \large\underbrace \color{blue}\bold {\theta \: = \: 48}$

Required trigonometric identity :—

$\large \bold {For \: \: any \: \: angle}\\ \bold{ {0}^{0} \leqslant x \leqslant {90}^{0}} \\ \\ \large\boxed{ \color{green}{ \bold{cos( {90}^{0} - x) = sin \: x}}}$

Answer 2

Answer:

θ = 24 degrees

Step-by-step explanation:

We know that sin(90-x) = cos x

Here , 90-x = 3θ , x=θ-6

(x)+(90-x)=90

=> (3θ) + (θ-6) = 90

=> 4θ=96

=> θ=24

Or you can remember this like : If the two angles are complementary , their sines and cosines are equal i.e , sin (90-x) = cos x or cos(90-x) = sin x

Hope this helps