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Question: If \(\sin\theta + \cos\theta = 1\), then \(\sin\theta\cos\theta =\)...

If sin⁡θ+cos⁡θ=1\sin\theta + \cos\theta = 1, then sin⁡θcos⁡θ=\sin\theta\cos\theta =

A

0

B

1

C

2

D

1/2

Answer

0

Explanation

Solution

sin⁡θ+cos⁡θ=1\sin\theta + \cos\theta = 1

Squaring on both sides, we get

⇒sin⁡2θ+cos⁡2θ+2sin⁡θcos⁡θ=1\Rightarrow \sin^{2}\theta + \cos^{2}\theta + 2\sin\theta\cos\theta = 1

∴sin⁡θcos⁡θ=0\therefore\sin\theta\cos\theta = 0.