Question

Simplify the trigonometric expression

Answer 1

D

Explanation:

The common multiple is (1 + sin(theta)) * (1 - sin(theta) )

Left fraction

Multiply top and bottom of the fraction by 1 - sin(theta)

`(1 - sin(\theta))/((1 - sin(\theta) ) * (1 + sin(\theta) ))`

`( 1 - sin(\theta))/(cos^2(\theta))`

Right Fraction

By the same method the right fraction gives.

`( 1 + sin(\theta))/(cos^2(\theta))`

Combine Left and Right Fractions.

`(1 - sin(\theta) + 1 + sin(\theta))/(cos^2(\theta))`

Answer:

`(2)/(cos^2(\theta))`

The actual answer out of those given is 2*sec^2(theta) which is D