Question

prove that;
${ \sin {}^{2} \alpha - \cos}^{2} \beta = \sin ^{2} \beta - \cos^{2} \beta$
please do it fast!!
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Answer 1

To prove : sin²@ - cos²ẞ = sin²ẞ - cos²@

Formula to be used : sin²∅ + cos²∅ = 1

sin²∅ = 1 - cos²∅

cos²∅ = 1 - sin²∅

Proof :

Taking LHS,

sin²@ - cos²ẞ

Applying mentioned formula,

(1 - cos²@) - (1 - sin²ẞ)

1 - cos²@ - 1 + sin²ẞ

sin²ẞ - cos²@ + 1 - 1

sin²ẞ - cos²@ = RHS

LHS = RHS

Hence, Proved!!

Note : Here @ is alpha, ẞ is beta and ∅ is theta.