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