[loire77]

cos^2x-cot^2x=cos^2xcot^2x

(1-cosx)/(1+cosx)=(cotx-cscx)^2

1/tanx-secx+1/tanx+secx=-2tanx

sec^4x-sec^2x=tan^4x+tan^4x

cosx/1-sinx=1+sinx/cosx

1-secxcosx=tanxcotx-1

sinx+cosx=secx+cscx/cscx+secx

sinx=sin^3+cos^2xsinx

sinx+cosx+1=2sinxcosx/sinx+cosx-1

[ebaines]

In almost all cases the way to approach these problems is to first convert tangent, cotangent, secant, and cosecant function to their sine and cosine equivalents, and then simplify the expression. You also may have to apply a few key identites that you must be familiar with, such as:

sin^2x +cos^2x = 1
sin2x = 2sinx cosx
cos2x = cos^2x - sin^2x = 2 cos^2x - 1 = 1 - 2 sin^2x

Memorize these and look for opportunities to apply them.

[MDAncell]

Verify
csc(x)cos^(2)(x)+sin(x)=csc(x)

[ebaines]

Verify
csc(x)cos^(2)(x)+sin(x)=csc(x)

See the advice given earlier in post #2 - it works well on this problem.

[elisa2520]

verify each

(sin 2x) (sec x) (csc x)=2

(sin 2x)^2=4 (1-sin^2 x-cos^4x)

prove:

sin 2x cosx=2 (sinx-sin3x)

[ebaines]

elisa2520: each of these can be solved if you apply the identity for sin(2x) - you should memorize this:



You will also have to apply the fundamental identity and its variations (e.g. ).