Question

prove that:
$\cos(\pi \div 4 - x) \cos(\pi \div 4 - y) - \sin(\pi \div 4 - x) \sin(\pi \div 4 - y) = \sin(x + y)$
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Answer 1

Step-by-step explanation:

LHS = cos(π/4 - x).cos(π/4-y)-sin(π/4 -x).sin(π/4-y)

Let ( π/4 -x) = A

(π/4 -y) = B

Then,

LHS = cosA.cosB -sinA.sinB

But we Know,

cos(A + B) = cosA.cosB-sinA.sinB

Using this,

= cos(A + B)

= cos{(π/4 -x)+(π/4 -y)}

=cos(π/2 -(x +y)}

We know,

Cos(π/2 -∅) = sin∅ use this ,

= sin(x + y) = RHS

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