Question

If sin 3$\theta$= cos($\theta$-${26}^{\circ }$), where 3$\theta$ and($\theta$-${26}^{\circ }$) are acute angles then find the value of $\theta$.

• A. 30^o
• B. 29^o
• C. 27^o
• D. 26^o

Answer 1

The correct option is B

29^o

$\Rightarrow$ sin 3$\theta$ =cos ($\theta -{26}^{\circ }$)

$\Rightarrow$ sin 3$\theta$ = sin $[{90}^{\circ }-(\theta -{26}^{\circ }\left)\right]$

$\Rightarrow$ 3$\theta$ = ${90}^{\circ }-\theta +{26}^{\circ }$

$\Rightarrow$ $\theta =\frac{{116}^{\circ }}{4}$

$\Rightarrow$ $\theta$ = ${29}^{\circ }$