Question

Find the value of
$sin(40^{\circ} + \theta) cos(10^{\circ} + \theta) - cos(40^{\circ} + \theta) sin(10^{\circ} + \theta)$.

• A. $1/2$
• B. $1/4$
• C. $1$
• D. $0$

Answer 1

Answer: (A)

We have,
$sin\left(40^{\circ}+ \theta\right)\cdot cos\left(10^{\circ} + \theta\right) - cos\left(40^{\circ} + \theta\right)\cdot sin\left(10^{\circ} + \theta\right)$
$=sin\left\{\left(40^{\circ}+\theta\right)-\left(10^{\circ}+\theta\right)\right\}$
$=sin30^{\circ}=\frac{1}{2}$