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Question
If A = B = 45° ,
show that:
cos (A + B) = cos A cos B - sin A sin B
Solution
Given that A = B = 45°
LHS = cos (A + B)
= cos ( 45° + 45°)
= cos 90°
= 0
RHS = cos A cos B – sin A sin B
= cos 45° cos 45° – sin 45° sin 45°
= `(1)/(sqrt2) (1)/(sqrt2) – (1)/(sqrt2) (1)/(sqrt2)`
= 0
LHS = RHS
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