Question

tan²(theta) = csc²(theta) tan²(theta) - 1​

Answer 1

Answer:

Given

tan2A + cot2 A = Sec2A Cosec2A - 2

Taking L.H.S.

⇒tan2A + cot2 A

⇒Sec2A - 1 + Cosec2A - 1 ( As we know 1 + tan2A = Sec2A , 1 + cot2A = Cosec2A )

⇒Sec2A + Cosec2A - 2

⇒1Cos2A + 1Sin2A - 2

⇒Sin2A + Cos2ACos2ASin2A - 2

⇒1Cos2ASin2A - 2

⇒Sec2A Cosec2A - 2

Hence

L.H.S. = R.H.S. ( Hence proved )