Question

If α + β – γ = π, then sin² α + sin² β – sin² γ is equal to ______.

पर्याय

• 2 sin α sin β cos γ

• 2 cos α cos β cos γ

• 2 sin α sin β sin γ

• None of these

Answer 1

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