how do i prove the following trig identities

Question

cotxsinx=cosx 

also tanxcotx-cos^2x=sin^2x

Answer 1

In general, try to work back to sine and cosine, and look for familiar identities such as sin^2 + cos^2 = 1.

cot x sin x = cos x

 

(cos/sin) * sin = cos

 

cos = cos

 

tan x cot x - cos^2 x = sin^2 x

 

(sin/cos)*(cos/sin) - cos^2 = sin^2

 

(Note that tan * cot = 1.)

 

1 - cos^2 = sin^2

 

1 = sin^2 + cos^2