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Question

If α is one of the principal solutions which satisfies the equation 1+sin2θ=3sinθcosθ, then which of the following is not possible?

A
sin2α=45
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B
cos2α=0
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C
sin3α=12
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D
cos3α=25
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Solution

The correct option is D cos3α=25
1+sin2θ=3sinθcosθ2sin2θ3sinθcosθ+cos2θ=0(sinθcosθ)(2sinθcosθ)=0sinθ=cosθ or 2sinθ=cosθtanθ=1 or tanθ=12
sin2α=2tanα1+tan2α=2×121+14=45

cos2α=0 (if tanα=1)

sin3α=sin135=12 (if tanα=1)

cos3α=4cos3α3cosα=4(25)33(25)
=255 (if tanα=12)




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