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.
Solve the following equation
tan (2x)+ sec (2x) = cos (x)+ sin (x)
Thanks for your help
8 answers
I am asked to solve this equation, not to prove this identities.
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
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
Ahhh, but in the original that would make it tan 90º which of course is undefined.
SO THERE IS NO SOLUTION TO YOUR EQUATION
SO THERE IS NO SOLUTION TO YOUR EQUATION
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.
tan (0)+ sec (0) = cos (0)+ sin (0)
0 + 1 = 1 + 0
Any multiple of 360 degrees will also work.
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 ??
btw , are drwls and reiny teachers or professors ??
Yes. One is a retired teacher; the other is a retired professor.
Actually I am a retired PhD physicist/engineer. I worked in the aerospace industry until 1992, and have been doing online tutoring since 1994.