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