Simplify sin(theta)-tan(theta)cos(theta)+cos(pi/2-theta)

$\sin (θ) - \tan (θ) \cos (θ) + \cos (\frac{π}{2} - θ)$

Step 1

Rewrite in terms of sines and cosines, then cancel the common factors.

Add parentheses.

$\sin (θ) - (\tan (θ) \cos (θ)) + \cos (\frac{π}{2} - θ)$

Rewrite $- \tan (θ) \cos (θ)$ in terms of sines and cosines.

$\sin (θ) - (\frac{\sin (θ)}{\cos (θ)} \cos (θ)) + \cos (\frac{π}{2} - θ)$

Cancel the common factors.

$\sin (θ) - \sin (θ) + \cos (\frac{π}{2} - θ)$

Step 2

Subtract $\sin (θ)$ from $\sin (θ)$ .

$0 + \cos (\frac{π}{2} - θ)$

Step 3

Add $0$ and $\cos (\frac{π}{2} - θ)$ .

$\cos (\frac{π}{2} - θ)$