Question

(sec A + tan A ) ( 1 -sin A)=?​

Answer 1

Step-by-step explanation:

$(sec A + tan A ) ( 1 -sin A) \\ = ( \frac{1}{cos \: A} + \frac{sin \: A}{cos \: A})( 1 -sin A) \\ = \frac{( 1 + sin A)}{cos \: A} ( 1 - sin A) \\ = \frac{( 1 + sin A ( 1 - sin A)}{cos \: A} \\ = \frac{1 - sin^{2} A}{cos \: A} \\ = \frac{cos^{2} \: A}{cos \: A} \\ = cos \: A. (\frac{cos \: A}{cos \: A} ) \\ = cos \: A \\ \times 1 \\ = cos \: A$

the required answer is

cosA

Ans