How do you prove 1+cot2x=cosec2x?
Proof of given relation:
1+cot2x=cosec2x
Here we have LHS=1+cot2x
Therefore,
1+cot2x=sin2xsin2x+cos2xsin2x [∵cotx=cosxsinx]
=sin2x+cos2xsin2x
=1sin2x [∵sin2x+cos2x=1]
=cosec2x [∵cosecx=1sinx]
=RHS
Hence, 1+cot2x=cosec2x is proved.