Question

Prove that cos ⁴a+2 cos²a(1-1/sec²a)=(1-sin⁴a)​

Answer 1

Answer:

LHS = RHS

Step-by-step explanation:

LHS = $cos^4A + 2cos^2A(1-cos^2A)$ = $cos^4A + 2cos^2A-2cos^4A$

      = $2cos^2A - cos^4A$ = $cos^2A (2-cos^2A)$ = $(1-sin^2A)(1+1-cos^2A)$

      = $(1-sin^2A)(1+sin^2A)$ = $(1-sin^4A)$ = RHS