Question

tan 70 - tan 20 = 2cot40
@mayankdevnani help pls ive been waiting for u

Answer 1

you have to prove this

Answer 2

ye

Answer 3

any ideas lol

Answer 4

i proved it....

Answer 5

convert whole equation into cot
use this formula :-
\[\large \bf \tan(90-A)=cotA\]
so we get,
\[\large \bf \cot20-\cot70\]
then use this :-
\[\large \bf cotA=\frac{\cos A}{sinA}\]
we get,
\[\large \bf \frac{\cos20}{\sin20}-\frac{\cos70}{\sin70}\]
then take LCM and simplify it,
\[\large \bf \frac{\sin70\cos20-\sin20\cos70}{\sin20\sin70}\]
we know that \(\large \bf sinAcosB-sinBcosA=\sin(A-B)\)
Use this,we get
\[\large \bf \frac{\sin(70-20)}{\sin20\sin70}\]
\[\large \bf \frac{\sin50}{\sin20\sin70}\]
Then,multiply and divide by 2,
\[\large \bf \frac{2\sin50}{2\sin20\sin70}\]
Use this,
\[\large \bf 2sinAcosB=\cos(A-B)-\cos(A+B)\]
we get,
\[\large \bf \frac{2\sin50}{\cos50-\cos90}\]
We know that cos90=0 and convert sin 50 into cos 40 by using this formula,sin(90-A)=cosA

After all ,we get
\[\large \bf \frac{2\cos40}{\cos50}\]
convert cos50 into sin40 [ cos(90-A)=sinA ]
we get,
\[\large \bf \frac{2\cos40}{\sin40}\]
we know that,
\[\large \bf farc{\cos40}{\sin40}=\cot40\]
using this,we get
\[\large \bf 2\cot40\]

\[\huge \cal \color{red}{Hence}~\color{Blue}{Proved} \color{green}{\smile}\]

Answer 6

@CrashOnce sorry...for taking too much time...

Answer 7

Here is my mistake:



i have corrected my mistake :-
we know that,
\[\large \bf \frac{\cos40}{\sin40}=\cot40\]

Answer 8

please go through this pic

Answer 9

wow amazing work @mayankdevnani I'm super impressed @-@ <3

Answer 10

thank you .....super impressed..lolz

Answer 11

you're welcome :) you must be a math major... really this proof @-@

Answer 12

oh!! thanks a lot

Answer 13

thanks so much!!!!!!!!!

Answer 14

welcome :)