Question

(sec A + tan A) (1 – sin A) =​

Answer 1

To solve:

            (sec A + tan A) (1 – sin A) =​

Solution:

         = (sec A + tan A) (1- sin A)

         =$(\frac{1}{cosA} +\frac{sinA}{cosA} ) (1-sin A)$

         $=(\frac{1+sinA}{cosA})(1-sinA)\\\\=\frac{(1+sinA)(1-sinA)}{cosA} \\\\=\frac{(1-sin^2A)}{cosA} \\\\=\frac{cos^2A}{cosA} \\\\=\frac{cosAXcosA}{cosA} \\\\=cosA$

∴(sec A + tan A ) (1-sinA) = cos A

Answer 2

Step-by-step explanation:

(sec A + tan A) (1 – sin A) =

= (1/cos S+ sinA/Cos A) (1 – sin A)

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

1-(sinA)^2/cos A

= (cos A) ^2/cos A

= cos A

(sec A + tan A) (1 – sin A) = cos A