Question

is this an identity?
10tanX/1+tan^2X=5sinX
i don't think it is.....?

Answer 1

Nope. not a standard identity

Answer 2

i tried alot of different things but i thought i might have done something wrong

Answer 3

\[\frac{10\tan ^{2} x}{\sec ^{2}x}\]change to sines and cosines and reduce

Answer 4

in fact it's wrong
\[\frac{10\tan x}{1+\tan^2 x}\]
\[\frac{10\tan x}{1+\frac{\sin ^2 x}{\cos^2 x}}\]
\[\frac{10\tan x\times \cos^2 x}{\cos^2 x+\sin ^2 x}\]
\[\frac{10\tan x\times \cos^2 x}{1}\]
\[10\times \frac{\sin x}{\cos x}\times \cos^2 x\]
\[10\times \sin x\cos x\]
\[5\times \underline {2 \sin x \cos x}\]
\[5\times \sin 2x\]

Answer 5

@jotwestmoreland do you get this?

Answer 6

let x=pi/4...
left side is \(\large \frac{10tan(\pi /4)}{1+tan^2(\pi /4)}=5 \)
right side is \(\large 5 \cdot sin(\pi /4)=\frac{5\sqrt2}{2} \)

Answer 7

There you go... lot's of ways to show that it just won't work.

Answer 8

if it was an identity, the left = the right ....

Answer 9

*for any x...

Answer 10

thank you all so much for confirming that!!

Answer 11

:D welcome