Question

if tanx+secx=e^x than sinx=??????

Answer 1

simplify tanx and sec x to their respective sinx and cosx form and solve for sinx ..
:)

Answer 2

(e^2x-1)/(e^2x+1)

Answer 3

\[tanx=\frac{ \sin x }{ \cos x }\] and \[\sec x=\frac{ 1 }{ \cos x }\]

Answer 4

now if you insert it you get it\[\frac{ 1+\sin x }{ cosx }= e ^{x}\]

Answer 5

final answer is right but how?

Answer 6

square both sides \[\frac{ (1+\sin x)^{2} }{ (cos x) ^{2} }\] now \[\cos ^{2}x=1-\sin ^{2}x\]
\[\frac{ (1+\sin x)^{2} }{ (1-\sin x)(1+sinx) }\]

Answer 7

Hasmukh

When you say final answer do u mean

sinx+1/cos x = e^x

or (e^2x - 1)
/(e^2x + 1)

Answer 8

so you will get \[\frac{ 1+sinx }{ 1-sinx }=e ^{2x}\]

Answer 9

e^2x-1/e^2x+1

Answer 10

@Hasmukh now i have given you sufficient hints you may try and you will ultimately learn out of it.......

Answer 11

or you can use compendo and dividendo to save urself from the labpur..
:D

Answer 12

1+sinx/1−sinx=e2x wrong 1/1-sinx=e^2x

Answer 13

thank u harsh314 will try

Answer 14

use compendo and dividendo my friend..

a/b = a+b/a-b

will help you solve it instantly!!
:D

Answer 15

are you studying derivatives in class?

Answer 16

@Hasmukh I'm asking you are you studying derivatives in class???

Answer 17

Helping my son

Answer 18

oh, then ask him if he is studying derivatives in class?

Answer 19

ok will ask

Answer 20

Ok anyways we have tan x + sec x =e^x right? And we need to find sinx
right?

Answer 21

yes

Answer 22

and also ask your ''Son'', if he has been studying logarithms in class?

Answer 23

ya

Answer 24

Ok, good. so...

Answer 25

he is in 11th

Answer 26

actually clarissa n u explain your way of reaching the answer..
I'm just curious to know how we can solve it using derivative Ihave an idea but will love to get a lil guide thrgh..
And since he is in 11th he wnt knw much abt derivatives or logs..
:P
As i've been thrgh the same academic curriculum

Answer 27

Alright, I'm trying to figure my way out of this. And I can surely help!

Answer 28

I will explain my method, but first let me do it myself in order to explain it to Hasmukh.

Answer 29

Me from Anand Gujarat

Answer 30

This seems like a very complex one.

Answer 31

why complex yar lets try will get it

Answer 32

A first step would be to turn everything into sines and cosines,
and see what that gives.

Answer 33

like tan =sin/cos
and sec=1/cos

Answer 34

I don't think they want you to use a calculator here,
It sounds like they want you to get an expression equal to sin(x), don't you think?

Answer 35

replace thte tan(x) with sin(x)/cos(x)

Answer 36

and the sec(x) with 1/os(x)
1/cos(x)

Answer 37

the goal is to get sin(x) = something
what might the next step be?