Question

if tan 2 theta =cot (theta +15) are acute , the value of theta is ​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{tan\,2\theta=cot(\theta+15^\circ)}$

$\underline{\textbf{To find:}}$

$\mathsf{The\;value\;of\;\theta}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Identity used:}}$

$\boxed{\mathsf{cot\,\theta=tan(90^\circ-\theta)}}$

$\mathsf{Consider,}$

$\mathsf{tan\,2\theta=cot(\theta+15^\circ)}$

$\mathsf{tan\,2\theta=tan(90^\circ-(\theta+15^\circ))}$

$\mathsf{tan\,2\theta=tan(90^\circ-\theta-15^\circ)}$

$\mathsf{tan\,2\theta=tan(75^\circ-\theta)}$

$\implies\mathsf{2\,\theta=75^\circ-\theta}$

$\implies\mathsf{2\,\theta+\theta=75^\circ}$

$\implies\mathsf{3\,\theta=75^\circ}$

$\implies\mathsf{\theta=\dfrac{75^\circ}{3}}$

$\implies\boxed{\mathsf{\theta=25^\circ}}$

Answer 2

tan 2 theta = cot (theta+15)

tan 2 theta =tan. (90-theta-15)

2 theta =75 - theta

2 theta +theta = 75

3 theta = 75

theta= 75÷3

theta= 25

Mark as brainiest plz