Hi. I'm struggling with a few questions - I seem to understand the trigonometric identities, but I'm not sure of the algebra. Can anyone please help solve the following equations (with steps and explanations, if possible):
1. VERIFY THE IDENTITY: sec^2 x sin^2 x - sec^2 x = -1
2. VERIFY THE IDENTITY: sin2x = 2tan x/1 + tan^2 x
3. SOLVE: 2sin^2 x-11cosx - 11 = 0, for 0 is less than or equal to x, which is less than 2 pi
4. SOLVE: 4sin x cos x - 2 square root 2sin x + 2cos x - square root 2 = 0, where x is a real number
5. VERIFY THE GIVEN IDENTITY: sin (x + y) sin (x - y) = sin^2 x - sin^2 y
Thank you!
1. VERIFY THE IDENTITY: sec^2 x sin^2 x - sec^2 x = -1
2. VERIFY THE IDENTITY: sin2x = 2tan x/1 + tan^2 x
3. SOLVE: 2sin^2 x-11cosx - 11 = 0, for 0 is less than or equal to x, which is less than 2 pi
4. SOLVE: 4sin x cos x - 2 square root 2sin x + 2cos x - square root 2 = 0, where x is a real number
5. VERIFY THE GIVEN IDENTITY: sin (x + y) sin (x - y) = sin^2 x - sin^2 y
Thank you!