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Question
Given A = 60° and B = 30°,
prove that : cos (A + B) = cos A cos B - sin A sin B
Solution
Given A = 60° and B = 30°
LHS = cos(A+B)
= cos(60° + 30°)
= cos90°
=0
RHS = cos A cos B – sin A sin B
= cos 60° cos 30° – sin 60° sin 30°
= `(1)/(2) (sqrt3)/(2) – (sqrt3)/(2) (1)/(2)`
=`(sqrt3)/(4) – (sqrt3)/(4)`
= 0
LHS = RHS
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