Mathematics
Prove the following identities :
(sec A - cos A)(sec A + cos A) = sin2 A + tan2 A
Trigonometric Identities
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Answer
By formula,
sec2 A = 1 + tan2 A
cos2 A = 1 - sin2 A
Solving L.H.S. of the equation
⇒ (sec A - cos A)(sec A + cos A)
⇒ sec2 A - cos2 A
⇒ 1 + tan2 A - (1 - sin2 A)
⇒ 1 - 1 + tan2 A + sin2 A
⇒ sin2 A + tan2 A.
Since, L.H.S. = R.H.S.,
Hence, proved that (sec A - cos A)(sec A + cos A) = sin2 A + tan2 A.
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