Asked by Anonymous
Write the expression in terms of costheta and then simplify.
cos^4theta - sin^4theta + sin^2theta
Ans: cos^4 θ - 1 - cos^4 θ + 1 - cos^2 θ
= -cos^2 θ
cos^4theta - sin^4theta + sin^2theta
Ans: cos^4 θ - 1 - cos^4 θ + 1 - cos^2 θ
= -cos^2 θ
Answers
Answered by
Reiny
cos^4 Ø - sin^4 Ø + sin^2 Ø
= (cos^2 Ø + sin^2 Ø)(cos^2 Ø - sin^2 Ø) + sin^2 Ø
= (1)(cos^2 Ø - sin^2 Ø) + sin^2 Ø
= cos^2 Ø
= (cos^2 Ø + sin^2 Ø)(cos^2 Ø - sin^2 Ø) + sin^2 Ø
= (1)(cos^2 Ø - sin^2 Ø) + sin^2 Ø
= cos^2 Ø