Question

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

please prove it .

Answer 1

taking the rhs part

1+Sina+Cosa/1+cosa- sina

dividing the numenator and denominator by cos a

= 1/cosa+sina/cosa+cosa/cosa whole divided by 1/cosa+cosa/cosa-sina/cosa

=seca+tana+1/ seca+1-tana

=seca+tana+(sec^2a-tan^2a)/seca+1-tana

=seca+tana+(seca+tana)(seca-tana)/seca+1-tana

taking seca +tana common

=seca+tana(1+seca-tana)/seca+1-tana

1+seca-tana in numerator and denominator will get cancelled

= seca+tana

now writing seca and tana in terms of sin and cos

we get,

1/cosa + sina/cosa

= 1+sina/ cosa

hence prooved

hope it helps!!!

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