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Question
If α + β – γ = π, then sin2 α + sin2 β – sin2 γ is equal to ______.
Options
2 sin α sin β cos γ
2 cos α cos β cos γ
2 sin α sin β sin γ
None of these
MCQ
Fill in the Blanks
Solution
If α + β – γ = π, then sin2 α + sin2 β – sin2 γ is equal to 2 sin α sin β cos γ.
Explanation:
sin2 α + sin2 β – sin2 γ
= sin2 α + sin (β – γ) sin (β + γ)
= sin2 α + sin (π – α) sin (β + γ) ...[∵ α + β – γ = π]
= sin α [sin α + sin (β + γ)]
= sin α [sin {π – (β – γ)} + sin (β + γ)]
= sin α [sin (β – γ) + sin (β + γ)]
= sin α [2 sin β cos γ]
= 2 sin α sin β cos γ
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Factorization Formulae - Trigonometric Functions of Angles of a Triangle
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