Question

Prove that (tana + seca-1)(cosa)/sina + cosa -1 = 1+sina / cosa​

Answer 1

Answer:

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Rationalising LHS

\dfrac{1+cos+sin} {1+cos-sin}1+cos−sin1+cos+sin × \dfrac{1+sin} {1+sin}1+sin1+sin

=> \dfrac{(1+cos+sin)(1+sin)}{1+cos-sin + sin+sin×cos-sin^2}1+cos−sin+sin+sin×cos−sin2(1+cos+sin)(1+sin)

=> \dfrac{(1+cos+sin)(1+sin)} {1+cos-(1-cos^2)+sin×cos}1+cos−(1−cos2)+sin×cos(1+cos+sin)(1+sin)

=> \dfrac{(1+cos+sin)(1+sin)} {cos+cos^2+sin×cos}cos+cos2+sin×cos(1+cos+sin)(1+sin)

=> \dfrac{(1+cos+sin)(1+sin)} {cos(1+cos+sin)}cos(1+cos+sin)(1+cos+sin)(1+sin)

=> \dfrac{1+sin} {cos}cos1+sin = RHS

Hence proved!!!

Hope it helps you