Question

if sin 2 theta=1/2 ,then cos(75 -theta)=?

Answer 1

Hi Mate!!?

Sin ( 2 x ) = Sin ( 30 )

=>. 2x = 30

=>. x = 15°

So,.


Cos ( 75 - 15 ) = Cos ( 60° )

=>. 1 /2

Have a nice time

Answer 2

Here I will use radians, if you want in degrees just multiply the angle in radians by
$\frac{180}{ \pi }$

Now , we are given that,
$\sin(2x) = \frac{1}{2}$
since,
$\sin(\pi - x) = \sin(x)$
We have two cases here,
$\sin(2x) = \frac{1}{2} \\ \sin(\pi - 2x) = \frac{1}{2}$
Take the inverse on both sides,
$2x = \frac{\pi}{6} \\ \pi - 2x = \frac{\pi}{6}$
Therefore we get,
$x = \frac{\pi}{12} + k\pi \\ x = \frac{5\pi}{12} + k\pi$
where k is a integer.
Now,
$\cos( \frac{5\pi}{12} - \frac{\pi}{12} ) = \cos( \frac{\pi}{3} ) = \frac{1}{2}$
and
$\cos( \frac{5\pi}{12} - \frac{5\pi}{12} ) = \cos(0) = 1$
These are the two values.
Note that these are values of the given expression when the angle is acute. As the angle is in form of theta+k*pi. The value of the given expression is plus/minus 1/2 or plus minus 1 with different integral values of k(since, cos(pi+x)= -cos(x))