Question

Prove that (tana+cota)^2 =sec^2 a+cosec^2a=sec^2a×cosec^2 a

Answer 1

Proof

L.H.S → (tanA + cotA)²

L.H.S → (tanA + 1/tanA)²

L.H.S → [(tan²A + 1)/tanA]²

L.H.S → (sec²A/tanA)²

L.H.S → (sec²A ÷ sinA/cosA)²

L.H.S → (sec²A × cosA/sinA)²

L.H.S → (1/cos²A × cosA/sinA)²

L.H.S → (1/cosA × 1/sinA)²

L.H.S → (secA × cosecA)²

L.H.S → sec²A × cosec²A = R.H.S

What about middle term?

Mid Term → sec²A + cosec²A

Mid Term → 1/cos²A + 1/sin²A

Mid Term → (sin²A + cos²A)/cos²A sin²A

Mid Term → 1/(cos²A sin²A)

Mid Term → 1/cos²A × 1/sin²A

Mid Term → sec²A × cosec²A = R H.S

Hence Proved