Question

if cos(alpha +bita)=0, then sin(alpha-bita) can be reduced to?​

Answer 1

given, $cos(\alpha+\beta)=0$

or, $cos(\alpha+\beta)=cos\frac{\pi}{2}$

or, $(\alpha+\beta)=k\pi+\frac{\pi}{2}$

where k is integer number.

if we assume k = 0

then, $(\alpha+\beta)=\frac{\pi}{2}$.......(1)

now, $sin(\alpha-\beta)$

= $sin(\alpha+\beta-2\beta)$

= $sin\left(\frac{\pi}{2}-2\beta\right)$ [ from equation (1) ]

[ we know as well, sin(π/2 - x) = cosx ]

= $cos2\beta$

hence, value of $sin(\alpha-\beta)$ can be reduced to $cos2\beta$

Answer 2

Step-by-step explanation:

cos 2 betta

hope this helps you