Question

.prove that cos (90-A).sinA + sin(90 - A).cosA = 1 ​

Answer 1

See Explanation

Explanation:

`cos (90-A).sinA + sin(90 - A).cosA = 1 \\ \\ LHS = cos (90-A).sinA + sin(90 - A).cosA \\ \\ = sinA.sinA + cosA.cosA\\ \\ = sin ^(2) A + cos^(2) A \\ \\ = 1 \\ \\=RHS\\\\ reason \\ cos (90- \theta) = sin \theta \\ sin (90- \theta) = cos \theta \\ sin ^(2) \theta + cos^(2) \theta = 1 \\ \\ thus \: proved \\`