Question

Prove the identity
1+sec a/sec a = sin^2a/1-cos a (Simplify LHS and RHS separately)

Answer 1

Step-by-step explanation:

substitute sec a for 1/cos a

1+1/cos a/1/cos a = cos a + 1/cos a × cos a / 1

cos a and cos a will get canceled and remaining will be 1 + cos a

RHS = sin^2a/1-cos a

multiply both numerator and denominator by 1 + Cosa

sin^2a(1+Cosa)/1^2 - cosa^2

we know that sin^2= 1^2 - cos^2

sin^2a(1+Cosa)/sin^2a

sin^2a will get cancelled and we will get Cosa+1

LHS=RHS