(1 + sinA)(1 – sinA)(1 + $$tan^2$$​A) is equal to:

Correct option is C

Given: ​

(1 + sinA)(1 – sinA)(1 + $$tan^2$$​A) 

Formula Used: ​

​$$1-\sin^2A = \cos^2 A \\ \ \\ 1+\tan^2A = \sec^2 A \\ \ \\ \cos A = \frac{1}{\sec A}$$​​

Solution: ​

​$$(1 + sinA)(1 – sinA)(1 + tan^2A) \\ \ \\ = (1^2 - \sin^2 A )(1 + \tan^2 A ) \\ \ \\ = ( 1 - \sin^2 A ) ( 1 + \tan ^2 A) \\ \ \\ =\cos^2 A \cdot \sec^2 A \\ \ \\ = \cos^2 A \times \frac{1}{\cos^2 A}\\ \ \\ = 1$$​​