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Question

If A = 60o and B = 30o, find the value of 
(sin A.cos B + cos A.sin B)2(cos A.cos B  sin A.sin B)2.


  1. 0

  2. -1

  3. 1

  4. 2


Solution

The correct option is C

1


Given: A = 60o and B = 30o

(sin A.cos B + cos A.sin B)2(cos A.cos B  sin A.sin B)2

=(sin 60o.cos 30o + cos 60o.sin 30o)2+
(cos 60o.cos 30o  sin 60o.sin 30o)2

=[(32×32)+(12×12)]2+
[(12×32)(32×12)]2

=[(34)+(14)]2+[(34)(34)]2

=[(34)+(14)]2+0

= 12=1

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