proving a trigonometric identity

[hot scroll]

hey, can I have a hint for this question? what rule should I use to get me started. i know that 1+tan^2(x) = sec^2(x) and that sinx/cosx = tanx but I don’t actually know what do with these rules to get me to 1

[lyric sail]

Does that cos mean cos theta?

what does it mean to $\equiv 1$

[azure spire]

k12byda5h

[hot scroll]

im assuming it does

[hot scroll]

wdym?

[lyric sail]

I just curious if it should be $=$ instead of $\equiv$

[azure spire]

k12byda5h

[hot scroll]

im not sure, we are just trying to prove that the left side can be written as the right side

[lyric sail]

oh ok

I don't think it is true

$$\frac{1}{1+\tan^2\theta} + \tan \theta = \frac{1+\tan\theta + \tan^3 \theta}{1+\tan^2 \theta}$$

[azure spire]

k12byda5h

[lyric sail]

If it is equivalent to 1

$$1+\tan\theta + \tan^3 \theta = 1+\tan^2 \theta$$ Therefore, $$1+tan^2\theta = \tan\theta$$

[azure spire]

k12byda5h

[lyric sail]

It is not true for all theta