Question

prove that (2+2sinx)/cosx = 2secx ???

Answer 1

what have you tried ?

Answer 2

is this really
\[\frac{2+2\sin(x)}{\cos(x)}=2\sec(x)\]?

Answer 3

this is crazy....

Answer 4

yup. so we don't need to solve it, only prove it. I had a bigger equation which I managed to simplify to the above, and I need it to equate to 2secx. I'm confused :P

Answer 5

because
\[\frac{2+2\sin(x)}{\cos(x)}=\frac{2}{\cos(x)}+\frac{2\sin(x)}{\cos(x)}=2\sec(x)+2\tan(x)\] and this is certainly not
\[2\sec(x)\] unless of course
\[\tan(x)=0\]

Answer 6

maybe you could post the original problem, because this is not correct

Answer 7

I had a bigger equation which I managed to simplify to the above, and I need it to equate to 2secx .... you should just type the whole equation ... hjahaha

Answer 8

okayy, lemme post the original question, okayy???

\[cosx/(1-sinx) + cosx/(1+sinx) = 2secx\]

Prove this.

Answer 9

how'd i guess?

Answer 10

not bad, broo.

Answer 11

numerator is
\[\cos(x)(1+\sin(x))+\cos(x)(1-\sin(x))=2\cos(x)\]
denominator is
\[1-\sin^2(x)=\cos^2(x)\]and then you are done by canceling

Answer 12

This is too easy, you should really try it out.

Answer 13

YUCK. I multiplied both the numerators with 1 + sinx, and not 2 different ones. YUCK. SLAP ME, SOMEONE.

Answer 14

xD

Answer 15

Slap slap slap ..

Answer 16

THANK YOU.

Answer 17

I got the answer. its easy. NCERT exercise type problem.

To Prove: cos x/ (1 - sin x) + cos x/(1+ sin x )= 2 sec x
Proof:
Cross multiplying, we get,
(cos x + cos x sin x + cos x - cos x sin x)/[ (1- sin x)(1 + sin x)]
= 2 cos x/(1 - sin square x)= 2 cos x/ cos x cos x= 2/ cos x = 2 sec x= RHS
Hence Proved.

Answer 18

Thanks FFM. Cheers