Answer:
D
Step-by-step explanation:
The common multiple is (1 + sin(theta)) * (1 - sin(theta) )
Left fraction
Multiply top and bottom of the fraction by 1 - sin(theta)
[tex]\dfrac{1 - sin(\theta)}{(1 - sin(\theta) ) * (1 + sin(\theta) )}[/tex]
[tex]\dfrac{ 1 - sin(\theta)}{cos^2(\theta)}[/tex]
Right Fraction
By the same method the right fraction gives.
[tex]\dfrac{ 1 + sin(\theta)}{cos^2(\theta)}[/tex]
Combine Left and Right Fractions.
[tex]\dfrac{1 - sin(\theta) + 1 + sin(\theta)}{cos^2(\theta)}[/tex]
Answer:
[tex]\dfrac{2}{cos^2(\theta)}[/tex]
The actual answer out of those given is 2*sec^2(theta) which is D
