Thread: Please help me with my proving identities

1. 1-sin x + 1-cos x = sin x + cos x-1
cos x sin x sin x cos x

2. sec^2x - tan^2 x + tan x = sin x + cos x
sec x

3. sin^3 x - sin x + cos x = cot x - cos^2 x
sin x

4. 1 + cot A + sec A _ tan A = sin A + cos A
csc A

Originally Posted by john edgar

1. 1-sin x + 1-cos x = sin x + cos x-1
cos x sin x sin x cos x

Hint: Multiply both sides of the equation by sin(x) cos(x) and then try it.

Originally Posted by john edgar

2. sec^2x - tan^2 x + tan x = sin x + cos x
sec x

Convert everything to sines and cosines:



Now add the fractions.

Originally Posted by john edgar

3. sin^3 x - sin x + cos x = cot x - cos^2 x
sin x

What's ? Hint: It's a familiar identity that has been slightly rewritten.

Originally Posted by john edgar

4. 1 + cot A + sec A _ tan A = sin A + cos A
csc A

Convert everything to sines and cosines and simplify:




-Dan