Question

(sec A + tan A) (1 − sin A) = ______.

विकल्प

• sec A

• sin A

• cosec A

• cos A

Answer 1

(sec A + tan A) (1 − sin A) = cos A.

Explanation:

The given expression is ${\displaystyle (\sec \text{A}+\tan \text{A})(1-\sin \text{A})}$.

Simplifying the given expression, we have

${\displaystyle (\sec \text{A}+\tan \text{A})(1-\sin \text{A})}$

= ${\displaystyle (\frac{1}{\cos \text{A}}+\frac{\sin \text{A}}{\cos \text{A}})(1-\sin \text{A})}$

= ${\displaystyle \frac{1+\sin \text{A}}{\cos \text{A}}\times (1-\sin \text{A})}$

= ${\displaystyle \frac{(1+\sin \text{A})(1-\sin \text{A})}{\cos \text{A}}}$

= ${\displaystyle \frac{1-{\sin }^2\text{A}}{\cos \text{A}}}$ 

= ${\displaystyle \frac{{\cos }^2\text{A}}{\cos \text{A}}}$

= ${\displaystyle \cos \text{A}}$