Question

Prove Sec(180/4 + A/2) sec( 180/4 + A/2)= 2secA​

Answer 1

Answer: Sec(180/4 + A/2) sec( 180/4 + A/2)= 2secA​

Explanation:

LHS = sec(π/4 +A/2)sec(π/4 - A/2)

1/cos(π/4+A/2)cos(π/4+A/2)

multiply and divide by 2

2/cos(2π/4) + cosA

we know that

2cosAcosB = cos(A+B) + cos(A-B)

2/cos(π/2) + cosA

2/0+cosA

2/cosA

2secA

So the final answer is 2secA

hence LHS = RHS