solve:
tantheta = sintheta
Well if theta is zero, that works :)
To solve the equation tan(theta) = sin(theta), we can use trigonometric identities to simplify the equation and find the possible solutions.
Using the definition of tangent and sine functions, we have:
tan(theta) = sin(theta)
By dividing both sides of the equation by cos(theta), which is the reciprocal of sin(theta), we get:
tan(theta) / cos(theta) = sin(theta) / cos(theta)
Using the identity tan(theta) = sin(theta) / cos(theta), we can substitute the left side of the equation:
tan(theta) / cos(theta) = tan(theta)
Now, we have:
tan(theta) = tan(theta)
The equation tan(theta) = tan(theta) is true for all real numbers of theta, except when cos(theta) equals zero. In other words, the possible solutions are all angles theta for which cos(theta) is non-zero.
Therefore, the solution to the equation tan(theta) = sin(theta) is all real numbers of theta except when cos(theta) equals zero.