Question

Prove That 2sin^pi/6 + cosec^7pi/6cos^pi/3 = 3/2

Answer 1

Your expression makes no sense
We use the ^ symbol as an exponent sign.

so your 2 sin^π/6 would be
2(sin)^(π/6) which is meaningless

if you simply meant:
2 sin(π/6) + cosec(7π/6)cos(π/3)
that would be
2(1/2) + (-2)(1/2) = 0

retype your problem.