Q24 of 118 Page 5

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

Given a = secx – tanx and b = cosecx + cotx

a and b

LHS = ab + a – b + 1

= 0 = RHS

Hence proved.

If cotx(1 + sinx) = 4m and cotx(1 – sinx) = 4n, prove that (m² – n²)² = mn.

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

Prove that :

where

If T_n = sinⁿx + cosⁿx, prove that