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Question

Prove that:
2sin2π6+cosec27π6cos2π3=32

Solution
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LHS=2sin2π6+cosec27π6cos2π3
=2sin2π6+cosec2(π+π6)cos2π3
=2sin2π6+cosec2(π6)cos2π3 ....As θ lies in the 3rd quadrant, θ is negative.

=2(12)2+(2)2×(12)2

=2×14+1 =32

= RHS

Hence proved.

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