How to Eliminate Exponents from Trigonometric Functions Using PowerReducing Formulas
Powerreducing formulas allow you to get rid of exponents on trig functions so you can solve for an angle’s measure. This ability comes in very handy in calculus.
At some point, you’ll be asked to rewrite an expression using only the first power of a given trig function — either sine, cosine, or tangent — with the help of powerreducing formulas, because exponents can really complicate trig functions in calculus when you’re attempting to integrate functions.
In some cases, when the function is raised to the fourth power or higher, you may have to apply the powerreducing formulas more than once to eliminate all the exponents. You can use the following three powerreducing formulas to accomplish the elimination task:
For example, follow these steps to express sin^{4 }x without exponents:

Apply the powerreducing formula to the trig function.
First, realize that sin^{4 }x = (sin^{2 }x)^{2}. Because the problem requires the reduction of sin^{4 }x, you must apply the powerreducing formula twice. The first application gives you the following:

FOIL the numerator.

Apply the powerreducing formula again (if necessary).
Because the equation contains cos^{2 }2x, you must apply the powerreducing formula for cosine.
Because writing a powerreducing formula inside a powerreducing formula is very confusing, find out what cos^{2 }2x is by itself first and then plug it back in:

Simplify to get your result.
Factor out 1/2 from everything inside the brackets so that you don’t have fractions both outside and inside the brackets. This step gives you
Combine like terms to get