Question

Select the correct option from the given alternatives :

If α + β + γ = π then the value of sin²α + sin²β – sin²γ is equal to …......

Options

• 2 sin α 

• 2 sin α cos β sin γ

• 2 sin α sin β cos γ

• 2 sin α sin β sin γ

Answer 1

2 sin α sin β cos γ

Explanation:

`sin^2alpha + sin^2 beta - sin^2γ`

= `(1 - cos2alpha)/2 + (1 - cos2beta)/2 - sin^2γ`

= `1 - 1/2(cos2alpha + cos2beta) - 1 + cos^2γ`

= `-1/2 xx 2cos(alpha + beta)cos(alpha - beta) + cos^2γ`

= cos γ cos (α – β) + cos^2γ  ...[∵ α + β + γ = π]

= cos γ [cos (α – β) + cos γ]

= cos γ [cos (α – β) – cos (α + β)]

= 2 sin α sin β cos γ