1. LS = (cos^2 x - 1)^2
= (-sin^2 x)^2
= sin^4 x
RS = (1-2 cos2x+cos^2 2x)/4
= (1 - cos^2 (2x))^2 / 4
= (1 - (1 - 2sin^2)^2 / 4
= (2sin^2 x)^2 / 4
= 4sin^4 x / 4
= sin^4 x
= LS
What is your progress for #2?
You might want to start with tan(π + 4x) = tan (4x)
= tan(2x + 2x) = 2 tan(2x)/(1 - tan^2 (2x) )
and again: tan (2x) = 2tanx/(1 - tan^2 x)
see what you can with that.
Prove:
1. (cos^2 x-1)^2=(1-2 cos2x+cos^2 2x)/4
2.tan(π+4x)=(4 tanx-4 tan^3 x)/(tan^4 x-6 tan^2 x+1)
2 answers
Prove: tan(π+4x)=(4 tanx-4 tan^3 x)/(tan^4 x-6 tan^2 x+1)