Question

If sin(theta+34)=costheta and(theta+34) is acute show that theta=28

Answer 1

$\textsf{Given:}$

$\mathsf{sin(\theta+34^{\circ})=cos\theta}$

$\textsf{Using,\boxed{cos\theta=sin(90^{\circ}-\theta)}}$

$\mathsf{sin(\theta+34^{\circ})=sin(90^{\circ}-\theta)}$

$\implies\mathsf{\theta+34^{\circ}=90^{\circ}-\theta}$

$\implies\mathsf{2\theta=90^{\circ}-34^{\circ}}$

$\implies\mathsf{2\theta=56^{\circ}}$

$\implies\boxed{\mathsf{\theta=28^{\circ}}}$