Question

Solve the following equation
tan (2x)+ sec (2x) = cos (x)+ sin (x)

Thanks for your help

Answer 1

your identity is false

just take x=30º

LS = tan60 + 1/cos60
=sqrt(3) + 2

RS = cos30 + sin30
= sqrt(3)/2 + 1/2 which is not= to the LS

To show an identity to be false, all you need is one exception.

Answer 2

I am asked to solve this equation, not to prove this identities.

Answer 3

blame it on the fact I did not have my second cup of coffee yet.

sin2x/cos2 + 1/cos2x = sinx + cosx
(2sinxcosx + 1)cos2x = sinx + cosx
(2sinxcos + sin^2x + cos^2x)/(cos^2x-sin^2) = sinx + cosx
(sinx+cosx)^2/(cos^2-sin^2) = sinx + cosx
(sinx + cosx)/[cosx-sinx)(cosx+sinx)] = sinx + cosx
crossmultiply
(sinx + cosx)^2 = (cosx+sinx)^2(cosx-sinx)
divide both sides by (cosx+sinx)^2
1 = cosx-sinx
sinx = cosx
divide by cosx
tanx = 1
x = 45º or 225º or pi/4, 5pi/4

Answer 4

Ahhh, but in the original that would make it tan 90º which of course is undefined.

SO THERE IS NO SOLUTION TO YOUR EQUATION

Answer 5

There is at least one solution: x = 0

tan (0)+ sec (0) = cos (0)+ sin (0)
0 + 1 = 1 + 0

Any multiple of 360 degrees will also work.

Answer 6

I've check my answer key and the answers are 0, 270 and 360. I cant figure out how to do it.
btw , are drwls and reiny teachers or professors ??

Answer 7

Yes. One is a retired teacher; the other is a retired professor.

Answer 8

Actually I am a retired PhD physicist/engineer. I worked in the aerospace industry until 1992, and have been doing online tutoring since 1994.