Question

if sin 2 theta =cos(theta-36°), 2theta and theta - 26° are acute angles then find the value of theta

Answer 1

Hey friend

Here is your answer

Sin2@=Cos(@-36°)

[•USING cos(90-@)=sin@]

Cos(90°-2@)=Cos(@-36)

90-2@=@-36

3@=90+36

3@=126

@=126/3

@=42

Hope this helps you

Answer 2

Given:

•  $sin3\theta=cos( \theta-26^\circ)$

• $2\theta$ and  $(\theta - 26^\circ)$  are acute angles.

To Find:

• The value of $\theta$

Solution:

    ⇒       $sin3\theta=cos( \theta-26^\circ)$

Using formula

         $cos \theta =sin(90^\circ - \theta )$

We get,

     ⇒      $sin3 \theta = sin[90^\circ-(\theta -26^\circ)]$

     ⇒      $3 \theta = [90^\circ-(\theta -26^\circ)]$

     ⇒     $3 \theta = 90^\circ- \theta + 26^\circ$

     ⇒     $3 \theta + \theta = 90^\circ + 26^\circ$

     ⇒     $4 \theta =116^\circ$

     ⇒     $\theta =29^\circ$

Thus, the value of $\theta =29^\circ$