Posted by **lina** on Tuesday, April 3, 2012 at 1:34pm.

Rewrite the expression so that it involves the sum or difference of only constants and sines and cosine to the 1st power

(sinx)^4

- pre-calculus -
**Steve**, Tuesday, April 3, 2012 at 3:32pm
sin^4

(1-cos^2)^2

(1-cos)^2(1+cos)^2

(1-cos)(1-cos)(1+cos)(1+cos)

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

so,

sin^4(x) = (1 - cos(2x))^2/4

= (1 - 2cos(2x) + cos^2(2x))/4

= (1 - 2cos(2x) + (1 - cos(4x))/2)/4

= (1 - 2cos(2x) + 1/2 - cos(4x)/2)/4

= (2 - 4cos(2x) + 1 - cos(4x))/8

= (3 - 4cos(2x) - cos(4x))/8

don't know which way you wanted to go there.

## Answer This Question

## Related Questions

- pre-calculus - Rewrite the expression so that it involves the sum or difference ...
- math - how do you rewrite the expression to the 1st power of cosine by using ...
- calculus - rewrite the expression in terms of the first power of the cosine. sin...
- Math - Rewrite the expression in terms of the first power of cosine sin^4(x)
- Pre-Calculus - How do you verify: 1.) sinxcosx+sinx^3secx=tanx 2.) (secx+tanx)/(...
- Trigonometry - rewrite the expression in terms of the first power of cosine. cos...
- Math - rewrite the expression in terms of the first power of cosine. cos^3(x)sin...
- Pre-calc - prove the identity: (cosx)(tanx + sinx cotx)=sinx+cos(squared)x i ...
- Mathmatics - a. Use the formulas for lowering powers to rewrite the expression ...
- PRE CALC - Which combination of limit properties is required to evaluate this ...

More Related Questions