Prove that tan(π/4 + x/2) = tanx + secx

Question

Prove that

tan\((\frac{\pi}{4}+\frac{x}{2})\) = tanx + secx

tan(π/4 + x/2) = tanx + secx

Answer 1

To Prove: tan\((\frac{\pi}{4}+\frac{\pi}{2})\) = tanx + secx

Proof: Consider L.H.S,

Multiply and divide L.H.S by cos\(\frac{x}{2}\) + sin\(\frac{x}{2}\)

∵ L.H.S = R.H.S,

Hence proved