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

That zero with the line through it is theta I believe.
Use the FOIL method to multiply the numerator and denominator out. Then use your Trig Identities (probably in your course content or notes already but you can also google them) to see what it is equal to.

Answer 2

Step-by-step explanation:

Here, we need to simplify the following expression :

$\dfrac{(1-cos\theta)(1+cos\theta)}{(1-sin\theta)(1+sin\theta)}$

Using the identity as :

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

$\frac{1-cos^2\theta}{1+sin^2\theta}$

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

= $\dfrac{sin^2\theta}{cos^2\theta}$

Since, $\dfrac{sin\theta}{cos\theta}=tan\theta$

So, $\dfrac{(1-cos\theta)(1+cos\theta)}{(1-sin\theta)(1+sin\theta)}=tan^2\theta$    

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