Question

Verify each identity:
cscx-sinx=cotxcosx

Answer 1

Step 1: Convert everything on left side to sin and cos.
Cscx - sinx ---> (1/sinx) - sinx
Step 2: Find common denominator. In this case, multiply sinx by (sinx/sinx) so the denominaor of both pieces will be sinx.
(1/sinx) - sinx -----> (1/sinx) - (sin^2x/sinx)
Step 3: Since they both have a common denominator, you can combine this into one fraction.
(1/sinx) - (sin^2x/sinx) ------> (1-sin^2x)/sinx
Step 4: Using a trig identity (cos^2x+sin^2x = 1), we know 1-sin^2x is equal to cos^2x.
(1-sin^2x)/sinx -----> cos^2x/sinx
Step 5: Okay, here's the funky part. You need to separate this into two fractions that multiply together to make a cotx and a cos x.
cos^2x/sinx -----> (cosx)(cosx/sinx)
Step 6: Cosx/sinx is equivalent to Cotx
(cosx)(cosx/sinx) ------> cosxcotx

Answer 2

thanks! :)

Answer 3

No problem! :)