trig identies

Question

1.prove each identity
sin (q)/1+sin (q)-sin q/1-sin(q)=-2 tan^ 2 (q)

 

2.(cos^2 q/1-sin q )- (cos^2/1+sin q)

Answer 1

Jsoh, let's do this!

 

a. First, we have to find a common denominator. Turns out we are just going to multiply the two denominators together. Our common denominator is (1 + sin(q))(1 - sin(q)) = 1 - sin²(q) = cos²(q)

 

We have to multiply each denominator times the other numerator now.

 

As an example, 1/5 + 2/3 = 1(3)/15 + 2(5)/15 = 3/15 + 10/15 = 13/15.

 

Soooo, (sin(q)(1 - sin(q)))/cos²(q) - (sin(q))(1 + sin(q)))/cos²(q) 

 

(sin(q) - sin²(q) - (sin(q) + sin²(q)))/cos²(q)

 

-2sin²(q)/cos²(q) = -2tan²(q)

 

b. You don't have all the info, but do it the same!