6 Trigonometry Questions needing help...

So I have like 6 problems right now left or so on my Calculus homework sheet (somewhere around like 150 problems total) and I'm having trouble showing these solutions.

Problem #1: Express sin(arccos x) in a form that contains no trigonometric functions or their inverses.

Problem #2: Use the trigonometric identity, sin(A+B) = (sin A cos B) + (cos A sin B), to verify that, sin2x = 2sin x cos x

Problem #3: Show that sin⁵ x cos⁴ x = sin⁵ x - 2sin⁷ x + sin⁹ x.

Problem #4: Show that sec³ x tan⁵ x = sec x tan x(sec⁶ x - 2sec⁴ x + sec² x).

Problem #5: Show that sin⁴ x = ³⁄₈ - ½cos 2x + ¹⁄₈cos 4x

Problem #6: Show that (1/1+ sin x) = sec² x - sec x tan x

And just to restate, that I'm sorry if it seems that I'm posting alot of questions on here but there is alot of problems and I do not have a book or any example problems to work off)

Thanks for any and all help.

Okay so I know that I'm a new member and all, and I'm sorry if it seems like