Question

True or False:$\tan \left(\theta \right)\cos \left(\theta \right)=\sin \left(\theta \right)$for any$\theta \ne \frac{(2k+1)\pi }{2}$

Short answer

The given statemen is true

Step-by-step solution

Given information

We are given$\tan \left(\theta \right)\cos \left(\theta \right)=\sin \left(\theta \right)for\theta \ne \frac{(2k+1)\pi }{2}$

explanation for true statement

We know that $\tan \left(\theta \right)=\frac{\sin \left(\theta \right)}{\cos \left(\theta \right)}Except\theta =\frac{(2k+1)\pi }{2}$

Hence

$$\begin{gathered} \frac{\sin \left(\theta \right)}{\cos \left(\theta \right)}\cos \left(\theta \right) \\ =\sin \left(\theta \right)Except\theta =\frac{(2k+1)\pi }{2} \end{gathered}$$

Hence the given statement is true statement.

Conclusion

Given statement is true statement