Question

(sec A + tan A)(1-sin A)=cos A prove

Answer 1

hay!!

Dear friend -


Hear is ur answer


(secA+tanA) (1-sinA) = cosA

LHS=>

First we multiply in both equations



=> secA+tanA-secA×sinA-tanA×sinA

$( \frac{1}{cosa}) + tana - tana - ( \frac{sin {}^{2}a }{cosa} )$

Hear we found tan a - tan a then we cut it

$( \frac{1}{cosa}) - ( \frac{sin {}^{2}a }{cosa} )$

we let the above equations in one brackets

$\frac{(1 - sin {}^{2} a)}{cosa}$

we know that formula (1-sin²A) = cos²A

so,

we put it value

$\frac{cos {}^{2}a }{cos \: a}$

And in last step we divide it by cos A and found our answer

$cos \: a$

Hence LHS = RHS proved

I hope it's help you