Complete the identity.
-$\sin ( 2 \theta ) \tan \theta + \cos ( 2 \theta ) =$ ?
A) $2 \cos ( 2 \theta )$
B) $\cos ( 3 \theta )$
C) 1
D) $\sec ( 2 \theta )$

Question

Quizplus · Accepted Answer

The identity can be simplified using trigonometric identities. $\sin(2\theta) = 2\sin(\theta)\cos(\theta)$ and $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$, so $\sin(2\theta)\tan(\theta) = 2\sin(\theta)\cos(\theta) \cdot \frac{\sin(\theta)}{\cos(\theta)} = 2\sin^2(\theta)$. Also, $\cos(2\theta) = 1 - 2\sin^2(\theta)$. Adding these gives $2\sin^2(\theta) + 1 - 2\sin^2(\theta) = 1$.

Complete the Identity sin⁡(2θ)tan⁡θ+cos⁡(2θ)=\sin ( 2 \theta ) \tan \theta + \cos ( 2 \theta ) =sin(2θ)tanθ+cos(2θ)=

Complete the Identity $\sin ( 2 \theta ) \tan \theta + \cos ( 2 \theta ) =$