Question

solve cos^4 theta-cos^2 theta​

Answer 1

Answer:

Step-by-step explanation:

You must know that cos^2theta is equal to 1-sin^2 theta

And sin^2theta is equal to 1-cos^2 theta

cos^4 theta-cos^2 theta

cos^2 theta(cos^2 theta-1)

cos^2 theta(1-sin^2 theta-1)

cos^2 theta(-sin^2 theta)

1-sin^2 theta(-sin^2 theta)

-sin^2 theta+sin^4 theta

sin^4 theta-sin^2 theta

Answer 2

Step-by-step explanation:

Explanation:

Start by replacing #4theta# with #2theta+2theta#

#cos(4theta) = cos(2theta+2theta)#

Knowing that #cos(a+b) = cos(a)cos(b)-sin(a)sin(b)# then

#cos(2theta+2theta) = (cos(2theta))^2-(sin(2theta))^2#

Knowing that #(cos(x))^2+(sin(x))^2 = 1# then

#(sin(x))^2 = 1-(cos(x))^2#

#rarr cos(4theta) = (cos(2theta))^2-(1-(cos(2theta))^2)#

# = 2(cos(2theta))^2-1#