Question

$sin(60+\theta )-cos(30-\theta )$ is equal to_____ if $(60+\theta )$ and $(30-\theta )$ are acute angles.

• A. 2 cos
• B. 2 sin
• C. 0
• D. 1

Answer 1

The correct option is C

0

We know, $(60+\theta )$ + $(30-\theta )$ = 90°

Therefore, $(60+\theta )$ = 90° - $(30-\theta )$

$sin({60}^{\circ }+\theta )$ - $cos({30}^{\circ }-\theta )$
=$sin({90}^{\circ }-({30}^{\circ }-\theta \left)\right)-cos({30}^{\circ }-\theta )$

=$cos({30}^{\circ }-\theta )-cos({30}^{\circ }-\theta )$
=0