Q11 of 44 Page 79

Find the value of x in the following:

cos x = cos 60° cos 30° + sin 60° sin 30°

We know that,


Cos(A - B) = cosAcosB + sinAsinB


Let A = 60°, B = 30°


Then,


cos 60° cos 30° + sin 60° sin 30°


= cos(A - B)


= cos(60° - 30° )


= cos30°


∴cos x = cos 60° cos 30° + sin 60° sin 30°


⇒ cos x = cos 30°


⇒ x = 30°


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