Question

If tanx + cot x = 2 then find the value of sin power 2n + cos power 2n x

Answer 1

tanx+cotx=2
=>tanx+1/tanx=2
=>(tan^2x+1)/tanx=2
=>tan^2x+1=2tanx
=>tan^2x-2tanx+1=0
=>(tanx-1)^2=0
=>tanx-1=0
=>tanx=1
=>tanx=tan45
=>x=45

sin^2n x+cos^2n x
=sin^2n 45+cos^2n 45
=(1/root2)^2n+(1/root2)^2n
=(1/root2+1/root2)^2n
=(2/root2)^2n
=(root2)^2×n
=2^n ans..