Question

The value of (sin 43° · cos 47° + sin 47° cos 43°) is ______.

Answer 1

The value of (sin 43° · cos 47° + sin 47° cos 43°) is 1.

Explanation:

sin 43° cos 47° + sin 47° cos 43°

= sin 43° cos(cos 90° – 43°) + sin(90° – 43°) cos 43°   ...[sin (90 – θ) = cos θ cos (90 – θ) = sin θ]

= sin 43° × sin 43° + cos 43° × cos 43°

= sin² 43° + cos² 43°

= 1