Question

Simplify ( 1 - cos0)( 1 + cos0) / ( 1 - sin0) ( 1 + sin0)

a. sin^2 0
b. cos^2 0
c. tan^2 0
d. cos0/sin0

(all the zeros have a line through them)

Answer 1

Explanation:

Here, we need to simplify the following expression :

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

Using the identity as :

`(a-b)(a+b)=a^2-b^2`

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

Since,
`sin^2\theta+cos^2\theta=1`

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

Since,
`(sin\theta)/(cos\theta)=tan\theta`

So,
`((1-cos\theta)(1+cos\theta))/((1-sin\theta)(1+sin\theta))=tan^2\theta`

So, the correct option is (c). Hence, this is the required solution.