Remember that tan = sin/cos. So your expression is sin/cos times cos. That's sin(theta).
Cos theta squared
cosec(q)*cot(q)*cos(q) = 1/sin(q)*cot(q)*cos(q) = cot2(q)
For a start, try converting everything to sines and cosines.
The side adjacent to theta divided by the hypotenuse, or the angle opposite of the right angle
- cos theta
By converting everything to sines and cosines. Since tan x = sin x / cos x, in the cotangent, which is the reciprocal of the tangent: cot x = cos x / sin x. You can replace any other variable (like thetha) for the angle.
cos(t) - cos(t)*sin2(t) = cos(t)*[1 - sin2(t)] But [1 - sin2(t)] = cos2(t) So, the expression = cos(t)*cos2(t) = cos3(t)
cos2(theta) = 1 so cos(theta) = Â±1 cos(theta) = -1 => theta = pi cos(theta) = 1 => theta = 0
(Sin theta + cos theta)^n= sin n theta + cos n theta
It is cotangent(theta).
Zero. Anything minus itself is zero.
The question contains an expression but not an equation. An expression cannot be solved.
The equation cannot be proved because of the scattered parts.
There can be no significant simplicfication if some of the angles are theta and others are x, so assume that all angles are x. [csc(x) - cot(x)]*[cos(x) + 1] =[1/sin(x) - cos(x)/sin(x)]*[cos(x) + 1] =1/sin(x)*[1 - cos(x)]*[cos(x) + 1] =1/sin(x)*[1 - cos2(x)] =1/sin(x)*[sin2(x)] = sin(x)
You can use the Pythagorean identity to solve this:(sin theta) squared + (cos theta) squared = 1.
cosine (90- theta) = sine (theta)
It's 1/2 of sin(2 theta) .
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.
The derivative of (sin (theta))^.5 is (cos(theta))/(2sin(theta))
The diagonal multiplied by sin(angle) gives one side of the rectangle and the diagonal times cos(theta) gives the other. So the area is (diagonal)2 x cos(theta) x sin(theta).
cos2(theta) = 1 cos2(theta) + sin2(theta) = 1 so sin2(theta) = 0 cos(2*theta) = cos2(theta) - sin2(theta) = 1 - 0 = 1