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If sin⁡2θ=cos⁡3θ and θ is an acute angle, then sinθ equals

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a

5−14

b

-5−14

c

5+14

d

-5−14

answer is A.

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Detailed Solution

sin⁡2θ=cos⁡3θ or 2sin⁡θcos⁡θ=4cos3⁡θ−3cos⁡θ or 2sin⁡θ=41−sin2⁡θ−3 or 4sin2⁡θ+2sin⁡θ−1=0 or sin⁡θ=5−14

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