Verified answer

TO PROVE THAT LHS = RHS

RHS= 3/2

LHS= 2sin²π/6+cosec²7π/6cos²π/3

= 2sin²π/6+cosec² (π+π/6) cos²π/3

= 2sin²π/6+cosec²(-π/6)cos²π/3

As θ lies in the 3rd quadrant, θ is negative.

=2 (½)²+(-2)²× (½)²

2×(¼)+1 = 3/2

hence proved that,

2sin²π/6+cosec²7π/6cos²π/3= 3/2

HOPE IT HELPS YOU