Mathematics
Prove the following identities :
(1 - tan A)2 + (1 + tan A)2 = 2sec2 A
Trigonometric Identities
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Answer
Solving L.H.S. of the equation :
⇒ (1 - tan A)2 + (1 + tan A)2
⇒ 1 + tan2A - 2tan A + 1 + tan2 A + 2tan A
⇒ 2 + 2tan2A
⇒ 2(1 + tan2A)
By formula,
1 + tan2A = sec2 A
⇒ 2sec2 A
Since, L.H.S. = R.H.S.
Hence, proved that (1 - tan A)2 + (1 + tan A)2 = 2sec2 A.
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