Q1.Reduce $\displaystyle sin^{4}\theta$ to an expression involving only function of multiples of $\displaystyle \theta$,raised to the first power.

Q2.How $\displaystyle 2cos^{2}\theta=1+cos2\theta$

I would also like to know how to reduce any function to the first power
thanks

Originally Posted by hacker804
Q1.Reduce $\displaystyle sin^{4}\theta$ to an expression involving only function of multiples of $\displaystyle \theta$,raised to the first power.

Q2.How $\displaystyle 2cos^{2}\theta=1+cos2\theta$

I would also like to know how to reduce any function to the first power
thanks
are you not familiar with the derivation of the double angle identity for cosine ?

$\displaystyle \cos(2t) = \cos(t + t) = \cos{t} \cdot \cos{t} - \sin{t} \cdot \sin{t} = \cos^2{t} - \sin^2{t}$

power reduction identities derived from this double angle identity for cosine ...

$\displaystyle \cos^2{t} = \frac{1+\cos(2t)}{2}$

$\displaystyle \sin^2{t} = \frac{1-\cos(2t)}{2}$