Explain these please

**hacker804** · August 1st 2012, 03:59 AM

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

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

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

**skeeter** · August 1st 2012, 04:08 AM

Originally Posted by hacker804

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

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

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 ?

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

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

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

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

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