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Question

The value of 1cos290+13sin250 is

A
34
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B
52
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C
43
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D
45
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Solution

The correct option is C 43
cos290=cos(270+20)=sin20
sin250=sin(27020)=cos20

1cos290+13sin250
=1sin2013cos20
=3cos20sin203cos20sin20=2[32cos2012sin20]3cos20sin20
=2[sin60cos20cos60sin20]3cos20sin20
=4sin(6020)23cos20sin20=4sin403sin40 (2sinθcosθ=sin2θ)=43

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