Question

1/secA+tanA=1-sinA/cosA

Answer 1

1/secA+tana=1-sina/cosA
1/1/cosa+sina/cosa=1-sina/cosa
1/1+sina/cosa=1-sina/cosa
cosa/1+sina=1-sina/cosa
cross multiply
cos^2a=1-sin^2a
cos^2a=cos^2a
LHS=RHS
hope its helpful

Answer 2

Step-by-step explanation:

LHS: 1/secA+tanA

=1/ [(1/cosA) + (sinA/cosA.)]

{secA=1/cosA. and tanA = sinA/cosA}

=1/1+sinA/cosA

=cosA/1+sinA

Now I can multiply both denominator and numerator with cosA

=cosA/1+sinA * cosA/cosA

= cos^2A/cosA+sinA.cosA

=1-sin^2A/ cosA+sinA.cosA

{cos^2A=1-sin^2A}

=(1-sinA)(1+sinA)/cosA(1+sinA)

Now, 1+sinA got cancelled from both numerator and denominator

= 1-sinA/cosA

Hence LHS=RHS proved

Hope it will help you!