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Question

Mathematics Question on Trigonometric Functions

If α,β\alpha , \beta are complementary angles, then cos⁡2 α+cos⁡2 β\cos^2 \, \alpha +\cos^2 \,\beta is equal to

A

0

B

1

C

-1

D

2

Answer

1

Explanation

Solution

α+β=180∘⇒β=180∘−α\alpha+\beta =180^{\circ} \Rightarrow \beta = 180^{\circ} -\alpha ∴   cos⁡β=sin⁡α\therefore \, \, \, \cos \beta = \sin \alpha cos⁡2 α+cos⁡2 β=cos⁡2 α+sin⁡2 α=1\cos^2 \, \alpha + \cos^2 \, \beta = \cos^2 \, \alpha + \sin^2 \, \alpha = 1