Question

prove that cot x-tan x/cos2x=cot x + tan x

Answer 1

\[2\cos^3 \theta /\cos \theta=1\]
\[2\cos ^2\theta=1 \]
\[\cos^2\theta=1/2\]
\[\cos \theta =1/\sqrt{2}\]
\[\theta=\cos^{-1}1/\sqrt{2} =\pi/4\]

Answer 2

Thanks Lucian

Answer 3

you're welcome!

Answer 4

Lucian I want help in this one too.

Answer 5

ok, take cot x+tanx to left hand side and cos2x to right by cross multiplying.
then you get\[\cot x- \tan x \div cotx+\tan x =\cos 2x\]
then convert cot x and tan x into sin and cos
you'll get a equation you recognize as one of the simplifications of cos2x

Answer 6

Thank you but wont that change the question? because I see that one on youtube

Answer 7

uh, not really, in the end you only have to prove that left hand side=right hand side. But if you want to do it another way, you can do this too: convert all the LHS elements into sin and cos, simplify. Once you get something you identify as some variation of the RHS elements, then convert the LHS into cot and tan