Trigonometric identities question

[knuckleheadnell]

The correct answer is A, but I do not know how to get that.

 

[Deleted member 4993]

View attachment 30128
The correct answer is A, but I do not know how to get that.

Can you express tan(x) in terms of sin(x) and cos(x) ?

Can you express tan(2x) in terms of tan(x) ?

 

[pka]

View attachment 30128
The correct answer is A, but I do not know how to get that.

This is a tricky numerical problem. May I suggest that you take note that $\dfrac{\pi}{2}\le\theta\le\pi$ so that $\theta\in\text{I\,I}$.
I would express $\tan(2\theta)$ in terms of $\sin(\theta)~\&~\cos(\theta)$.
I expect you to the other values.

 

[P.K.Tandon]

 

[Deleted member 4993]

View attachment 30325

It would be better if you could copy and past your attachment. We generally don't like to open unknown attachments.