do this sin120/cos45= tan(4x+90). then take the inverse tangent. should give you tan^-1(sin120/cos45) = 4x+90. You should have a whole number for the left side then just do simple algebra and subtract 90 from the left side and then divide by 4 and you should have your answer.
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Verified answer
sin x - cos x - tan x = -1
sin x - cos x = tan x - 1
sin x - cos x = (sin x / cos x) - 1
sin x - cos x = (sin x / cos x) - (cos x / cos x)
sin x - cos x = (sin x - cos x) / cos x
cos x (sin x - cos x) = sin x - cos x
cos x = (sin x - cos x) / (sin x - cos x)
cos x = 1
x = 0 degrees
to check:
sin 0 - cos 0 - tan 0
= 0 - 1 - 0
= -1
True.
However, the above process assumed that sin x - cos x did not equal zero, so we have to take that possibility into account also.
sin x - cos x = 0
sin x = cos x
x = 45 degrees.
Is that also a solution?
sin 45 - cos 45 - tan 45
= (sqrt 2 / 2) - (sqrt 2 / 2) - 1
= -1
*******************************
So, there are two answers (in the 0 - 90 degrees interval)
x = 0 and x = 45
Men...
Well I Will give you one real answer...
six x - cos x - tg x = -1
sin x - cos x - (sin x / cos x) = -1
(sinx cos x - cos² x - sin x ) / cos x = -1
(sinx cos x - cos² x - sin x ) = -cos x
(sinx cos x - sin x ) = cos ² x -cos x
sinx (cos x - 1 ) = cos x (cos x - 1)
sinx (cos x - 1 ) - cos x (cos x - 1) = 0
(sinx - cos x )(cosx - 1) = 0
sin x - cos x = 0 => sin x = cos x
or
cos x - 1 = 0
cos x = 1
The angles that sin x = cos x are 45º =π/4+ kπ
The angles that cos x = 1 are kπ
for k=0,1,...
for example, for k = 0
π/4+ kπ = π/4
sin π/4 - cos π/4- tg π/4 = √2/2 - √2/2 - 1 = -1 (OK)
kπ = 0
sin 0 - cos 0- tg 0 = 0 - 1 - 0 = -1 (OK)
So:
x = {π/4+ kπ; k =0,1,2...}
or
x = {kπ; k =0,1,2...}
Kisses from Brazil
=**
do this sin120/cos45= tan(4x+90). then take the inverse tangent. should give you tan^-1(sin120/cos45) = 4x+90. You should have a whole number for the left side then just do simple algebra and subtract 90 from the left side and then divide by 4 and you should have your answer.
sin(0) = 0
cos(0) = 1
tan(0) = 0
sin(0) - cos(0) - tan(0) = -1
Not sure if this helps at all, but it works. :-) Feel free to e-mail me if you have more trig questions.
I have kept Trig as Optional So Sorry......
I don't know the answer, but I'm thankful I don't have to do those things anymore! Good luck!
It means that you will have to come over to my MAN-CAVE and we will have to rename you MENDED HEART , then we can work out the arithmetic .
take x=0
and then we get -1 answer
Wow if thats your pic then you look good!!
youre gorgeous.