Write an equivalent expression for cos^4 theta that does not involve any powers of sin or cosine greater then 1.

Question

asked Mar 1, 2021 154k views

1 Answer

Nika · Answer 1 · 2021-03-07T04:47:36+0000

Answer:

$cos^4\Theta =(1)/(4)(2+(cos4\Theta )/(2)+2cos\Theta  )$

Explanation:

We have given
$cos^4\Theta$

We have to find the expression in which there is no term of sine or cos of power more than 1

So
$cos^4\Theta =cos^2\Theta * cos^2\Theta$

We know that
$cos2\Theta =2cos^2\Theta -1$

$cos^2\Theta =(1+cos2\Theta )/(2)$

So
$cos^4\Theta =(1+cos2\Theta )/(2)* (1+cos2\Theta )/(2)$

$cos^4\Theta =(1)/(4)(1+cos2\Theta )^2$

$cos^4\Theta =(1)/(4)(1+cos^22\Theta+2cos\Theta  )$

$cos^4\Theta =(1)/(4)(1+(1+(cos4\Theta )/(2))+2cos\Theta  )$

$cos^4\Theta =(1)/(4)(2+(cos4\Theta )/(2)+2cos\Theta  )$