Prove the identity : ( sec A + cos A)( sec A-cos A) = tan A ^2+ sin A^2
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Answered by
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L.H.S = (secA +cosA)(secA-cosA)
= sec^2 -secAcosA + cosAsecA -cos^2
= (tan^2A + 1) - (1 - sin^2A)
=tan^2A + 1 - 1 + sin^2A
= tan^2A + sin^2A = RHS
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Answered by
7
Answer:
Step-by-step explanation:
L.H.S = (secA +cosA)(secA-cosA)
= sec^2 -secAcosA + cosAsecA -cos^2
= (tan^2A + 1) - (1 - sin^2A)
=tan^2A + 1 - 1 + sin^2A
= tan^2A + sin^2A = RHS
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