Subtract the following?

Question

How do you do this..?
(1+sin(x)/cos(x)
- (cos(x)/1+sin(x))

A. 2sec(x)
B. 2tan(x)
C. 2cot(x)
D. 2csc(x)

Answer 1

(1 + sin x) / cos x - cos x / (1 + sin x)

= [ (1 + sin x ) ² - cos² x ] / cos x (1 + sin x)

= [1 + 2sin x + sin² x - cos² x ] / cos x(1 + sin x)

= [ 2 sin² x + 2sin x ] / cos x (1 + sin x)

= 2sin x(sin x + 1) / cos x (1 + sin x)

=2 sin x / cos x

= 2 tan x which is answer B

Answer 2

the answer is b, 2tan(x)