With Reference to the standard right angle triangle, show that cosec^2 x =1+cot^2 x

Question

Using Pythagoras, and making reference to a right angle triangle.  

Answer 1

(csc x)²  =  1  +  (cot x)²

 

Convert to sines and cosines

 

 1 / (sin x)²  =  1  +  (cos x)² / (sin x)²

 

Multiply both sides by (sin x)²

 

1  =  (sin x)²  +  (cos x)²  ... which is an identity

 

1 = 1