Please show how to do these problems so i understand.

Question

1)Prove that sin^2 x (1+cot^2 x)=1

2)Prove that tan x (cot x+tan x)=sec^2 x

Answer 1

I find that changing everything to sines and cosines usually works well for these type of problems
unless you recognize one of the standard formulas.

LS = sin^2 x (1 + cos^2 x/sin^2 x)
= sin^2 x (sin^2 x + cos^2 x)/sin^2 x , forming a common denominator
= sin^2 x (1/sin^2 x)
= 1
= RS

try the second one using a similar method