If $\;\alpha + \beta - \gamma = \pi ,\,\;{\rm{then}}\,\,{\sin ^2}\,\,\alpha + {\sin ^2}\,\,\beta - {\sin ^2}\,\,\gamma \;$ is equal to

$2\,\,\cos \,\,\alpha \,\,\cos \beta \,\,\cos \,\,\gamma $

$2\,\,\sin \,\,\alpha \,\,\sin \beta \,\,\sin \,\,\gamma $

JEE MATHEMATICS MCQ: TRANSFORMATIONS

1 Easy

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Application +4 | -1

\;\alpha + \beta - \gamma = \pi ,\,\;\mathrm{then}\,\,{\sin ^2}\,\,\alpha + {\sin ^2}\,\,\beta - {\sin ^2}\,\,\gamma \;

is equal to

View answer and explanation

Correct option: A

2\,\,\sin \,\,\alpha \,\,\sin \beta \,\,\cos \,\,\gamma

Option A,

2\,\sin \,\alpha \,\sin \beta \,\cos \,\gamma

, is correct because it is the simplified form of the given expression using trigonometric identities and the given condition

\;\alpha + \beta - \gamma = \pi

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