Question #915b6
1 Answer
Use the identity
Explanation:
- First: solving
(sin^2theta+cos^2theta)^3=(1)^3
(sin^2theta+cos^2theta)(sin^4theta+2sin^2theta*cos^2theta+cos^4theta)=1
-
Using a the same method starting with
(sin^2theta+cos^2theta)^2=(1)^2
you get:
sin^4theta+cos^4theta=1-2[sin^2theta*cos^2theta] -
The left side of the equation
=
2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta)+1
=2(1-3sin^2theta*cos^2theta)-3(1-2sin^2theta*cos^2theta)+1
=2cancel(-6sin^2theta*cos^2theta)-3+cancel(6sin^2theta*cos^2theta)+1
=2-3+1 =0