Q25 of 118 Page 5

Prove that :
where

LHS

[∵ π/2 <x < π and in second quadrant, cosx is negative]

= RHS

Hence proved.

If sinx + cosx = m, then prove that sin⁶x + cos⁶x = where m² ≤ 2

If a = secx – tanx and b = cosecx + cotx, then show that ab + a – b + 1 = 0.

If T_n = sinⁿx + cosⁿx, prove that

2 T₆ – 3 T₄ + 1 = 0