It's 1/2 of sin(2 theta) .
The derivative of (sin (theta))^.5 is (cos(theta))/(2sin(theta))
It is 2*sin(theta)*sin(theta) because that is how multiplication is defined!
For such simplifications, it is usually convenient to convert any trigonometric function that is not sine or cosine, into sine or cosine. In this case, you have: sin theta / sec theta = sin theta / (1/cos theta) = sin theta cos theta.
(Sin theta + cos theta)^n= sin n theta + cos n theta
sin (theta) = [13* sin (32o)]/8 = 13*0.529919264/8 = 0.861118804 [theta] = sin-1 (0.861118804) [theta] = 59.44o
2 sin^2 theta = 1/4 sin^2 theta = 1/8 sin theta = sqrt(1/8) theta = arcsin(sqrt(1/8))
It is not! So the question is irrelevant.
Sin theta of 30 degrees is1/2
(/) = theta sin 2(/) = 2sin(/)cos(/)
Remember that tan = sin/cos. So your expression is sin/cos times cos. That's sin(theta).
You can use the Pythagorean identity to solve this:(sin theta) squared + (cos theta) squared = 1.