Express sin theta in terms of tan theta

General
1

express sin theta in terms of tan theta

2

To express sin theta in terms of tan theta, we can use the trigonometric identity:

sin^2(theta) + cos^2(theta) = 1

Let’s rearrange this equation to solve for sin theta:

sin^2(theta) = 1 - cos^2(theta)

Now, we can express cos theta in terms of tan theta using the identity:

cos^2(theta) = 1 / (1 + tan^2(theta))

Substituting this into the previous equation:

sin^2(theta) = 1 - (1 / (1 + tan^2(theta)))

Taking the square root of both sides:

sin(theta) = sqrt(1 - (1 / (1 + tan^2(theta))))

Therefore, sin theta can be expressed in terms of tan theta as:

sin(theta) = \sqrt{(1 - (1 / (1 + tan^2(theta))))}