Answer:
[tex]cos^4\Theta =\frac{1}{4}(2+\frac{cos4\Theta }{2}+2cos\Theta )[/tex]
Step-by-step explanation:
We have given [tex]cos^4\Theta[/tex]
We have to find the expression in which there is no term of sine or cos of power more than 1
So [tex]cos^4\Theta =cos^2\Theta \times cos^2\Theta[/tex]
We know that [tex]cos2\Theta =2cos^2\Theta -1[/tex]
[tex]cos^2\Theta =\frac{1+cos2\Theta }{2}[/tex]
So [tex]cos^4\Theta =\frac{1+cos2\Theta }{2}\times \frac{1+cos2\Theta }{2}[/tex]
[tex]cos^4\Theta =\frac{1}{4}(1+cos2\Theta )^2[/tex]
[tex]cos^4\Theta =\frac{1}{4}(1+cos^22\Theta+2cos\Theta )[/tex]
[tex]cos^4\Theta =\frac{1}{4}(1+(1+\frac{cos4\Theta }{2})+2cos\Theta )[/tex]
[tex]cos^4\Theta =\frac{1}{4}(2+\frac{cos4\Theta }{2}+2cos\Theta )[/tex]
