Question

The value of (sin 20° cos 70° + sin 70° cos 20°) is ______.

Answer 1

The value of (sin 20° cos 70° + sin 70° cos 20°) is 1.

Explanation:

sin 20° cos 70° + sin 70° cos 20°

⇒ sin 20° cos (90° – 20°) + sin (90° – 20°) cos 20°   ...`[(∵ sin (90 + θ) = cos θ),(cos (90 - θ) = sin θ)]`

⇒ sin 20° · sin 20° + cos 20° · cos 20°

⇒ sin²20° + cos²20° = 1   ...(sin²θ + cos²θ = 1)