Trigonometrical confusion!

Geometry Level 2

If $\alpha$ + $\beta$ = $\large\frac{\pi}{2}$ and $2$ [ $cos^{2}$ $\alpha$ $-$ $cos^{2}$ $\beta$ ] = $1$ , then find the value of $\alpha$ .

Assume $0\leq \alpha \leq\frac\pi2$ .

\frac{\pi}{2}

\frac{\pi}{6}

\frac{\pi}{4}

\frac{\pi}{3}

1 solution

Raj Rajput
Aug 11, 2015

How come $cos^{2}\alpha$ $-$ $sin^{2}\alpha$ = $cos2\alpha$ ? Please explain Raj Rajput .

Actually we have not been taught this yet.

Sahba Hasan - 5 years, 10 months ago

its an identity , for its proof write as cos(a+a) = cos2a (apply cos(a+b) = cosacosb - sinasinb ) you will get the result

RAJ RAJPUT - 5 years, 10 months ago

you got to learn a new thing from here :) but i have done it without that identity too

RAJ RAJPUT - 5 years, 10 months ago