Question

prove that sec a (1-sin a) (sec a + tan a) =1

Answer 1

seca(1-sina)(1/cosa+Sina/cosa)

=> seca(1-sina)(1-sina)/cosa

=> seca(1-sin²a)/cosa

=> seca cos ²a/cosa

=> 1/cos a×cosa

=1
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Answer 2

Answer:

Step-by-step explanation:

L.H.S=sec a (1-sin a)(sec a + tan a)

=1/cos a(1-sin a)(1/cos a+sin a/cos a)

=(1-sin a)(1+sin a)/cos a×cos a

As we know, (a-b)×(a+b)=a^2-b^2

=(1^2- sin^2a)/cos^2a

=cos^2a/cos^2a {sin^2a+cos^2a=1,

cos^a=1-sin^a}

=1.

Hence, L.H.S = R.H.S

PROVED.