Question

PLEASE HELP!! RSM in 2 days and trig is not my thing.

1) (2sin^2a-1)/(sina+cosa)
2)(sin^2a+1)cot^2a-csc^2a

Answer 1

To simplify the expression (2sin^2a-1)/(sina+cosa), you can use trigonometric identities and properties. First, rewrite sin^2a as (1 - cos^2a) using the Pythagorean identity. Then, simplify the expression further using various trigonometric identities.

Step-by-step explanation:

To simplify the expression (2sin^2a-1)/(sina+cosa), we can use trigonometric identities and properties.

1. First, let's rewrite sin^2a as (1 - cos^2a) using the Pythagorean identity.
2. Substituting this in the numerator, we have (2(1 - cos^2a) - 1) / (sina + cosa).
3. Simplifying further, we get (1 - 2cos^2a) / (sina + cosa).
4. Now, we can factor out a negative sign from the numerator to get -2(cos^2a - 1/2) / (sina + cosa).
5. Using the identity cos^2a - 1/2 = -sin^2 (pi/2 - a), we can rewrite the expression as -2sin^2(pi/2 - a) / (sina + cosa).
6. Finally, we can further simplify the expression as -2sin(pi/2 - a) / (sina + cosa).