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If \( \Large sin \ \theta + cos \ \theta =1 \), what is the value of \( \Large sin \ \theta \ cos \ \theta \)?

A) 2
B) 0
C) 1
D) 1/2

Correct Answer:


B) 0

Description for Correct answer:
\( \Large sin \theta +cos \theta =1 \)

On squaring both sides, we get

\( \Large (sin \theta +cos \theta)^{2} =1 \)

\( \Large sin^{2} \theta +cos^{2} \theta +2 \ sin \theta cos \theta =1 \)

\( \Large 1+2sin \theta cos \theta =1 \)

\( \Large 2sin \theta cos \theta =0 \)

\( \Large sin \theta cos \theta =0 \)

Part of solved Trigonometry questions and answers : >> Elementary Mathematics >> Trigonometry

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