Question

1) ctgx+cosx=1+ctgx*cosx

2) sin^4x+cos^4x=1/2

3) (sinx-cosx)^2=sin2x

4) sin^4x-cos^4x=7/2(sinxcosx)

5) sin^2x-sinxcosx+cosx-sinx=0

Answer 1

How about you try first and post your results.

Answer 2

2) sin^4x+cos^4x=1/2
sin^2x*sin^2x+cos^4x=1/2
(1-cos^2x)(1-cos^2x)+cos^4x=1/2
1-cos^2x-cos^2x+2cos^4x=1/2
2cos^4x-2cos^2x+1=1/2
2cos^4x-2cos^2x+1/2=0
x=pi/4+2kpi x2=7pi/4+2kpi