cot x sec4x = cot x + 2 tan x + tan3x

Question

anonymous · Answer

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

loser66 · Answer

hahaha. the problem was in 1 month ago!!!!??? still need help???

zzr0ck3r · Answer

how Is that funny?

loser66 · Answer

To me, if I am stuck and need help, I come here to make question. If I don't get answer in 3 days, the problem is solved in class for sure. How can it last 1 month?

anonymous · Answer

I still need it to be explained because I'm going over the things I didn't understand.

anonymous · Answer

If someone could explain how to do this that would be wonderful

loser66 · Answer

ok, I am so sorry friend, let me see whether I can help or not.

loser66 · Answer

yours is $$cot xsec^4x = cotx -2 tan x +tan^3 x$$ Prove or solve?

anonymous · Answer

Prove

loser66 · Answer

$$sec^4x = (sec^2x)^2 = (1+tan^2x)^2$$

loser66 · Answer

and then $$(1+tan^2x)^2 = 1 +2 tan^2x + tan^4 x$$

loser66 · Answer

you still have cot x in the front of them, now, let the whole thing be 
$$cot x (1 +2 tan^2x +tan^4 x= cot x +2 cot x tan^2 x +cot x tan^4x$$
on the other hand, you have $$cot x= \frac{1}{tanx}$$ therefore
yours = $$cotx +2 tanx +tan^3 x$$ the problem is proven

loser66 · Answer

I compensate for my fault when laughing at the time of the question. Forgive me?

anonymous · Answer

Thank you :)

loser66 · Answer

Please, feel free to make question if there is any