This discussion is closed.
Kurdt Morelo
Badges: 0
#1
Report Thread starter 16 years ago
#1
Prove that for all values of x


(2 tan x) - (sin 2x) = 2sin(squared)xtan x



thanks!
0
Kurdt Morelo
Badges: 0
#2
Report Thread starter 16 years ago
#2
anyone?
0
mikesgt2
Badges: 0
Rep:
?
#3
Report 16 years ago
#3
RHS = 2sin^2(x)tan(x) = 2(1-cos^2(x))tan(x) = 2(tan(x) - cos(x)sin(x)) = 2tan(x) - 2sin(x)cos(x) = 2tan(x) - sin(2x) = LHS
0
HammaL
Badges: 11
Rep:
?
#4
Report 16 years ago
#4
(Original post by Kurdt Morelo)
Prove that for all values of x


(2 tan x) - (sin 2x) = 2sin(squared)xtan x



thanks!
2 tan x - Sin 2x = 2 Sin ^2 x . tan x
2 Sin x/Cos x - 2 Sin x Cos x = 2 Sin ^2 x . (Sin x/ Cos x)
2 Sin x .[(1/cos x) - cos x ] = 2 Sin x .(Sin ^2 x / Cos x)
[(1-cos ^ 2x)/cos x] = Sin ^2 x / Cos x
cos ^2 x = 1 - Sin ^2 x
So :
[(1-1+Sin ^2 x)/cos x] = Sin ^2 x/ Cos x
Sin ^2 x / cos x = Sin ^2 x / cos x
0
Kurdt Morelo
Badges: 0
#5
Report Thread starter 16 years ago
#5
mikes gt2:


2(1-cos^2(x))tan(x) = 2(tan(x) - cos(x)sin(x))

how do you work that out?

thanks
0
mikesgt2
Badges: 0
Rep:
?
#6
Report 16 years ago
#6
(Original post by Kurdt Morelo)
mikes gt2:


2(1-cos^2(x))tan(x) = 2(tan(x) - cos(x)sin(x))

how do you work that out?

thanks
2(1-cos^2(x))tan(x) = 2( tan(x) - cos^2(x)tan(x) )

Now, cos^2(x)tan(x) = cos^2(x)[ sin(x)/cos(x) ] = cos(x)sin(x). So,

2( tan(x) - cos^2(x)tan(x) ) = 2( tan(x) - cos(x)sin(x) )

I hope this helps.
0
KELLARY LEUNG
Badges: 0
#7
Report 16 years ago
#7


LHS:
2tan2x-sin2x
= 2( sinx/cosx ) - 2sinxcosx
= [2sinx-2sinxcos(square)x]/cosx
= 2sinx[1-cos(square)x]/cosx
= 2sin(square)xtanx
= RHS
0
X
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

If you do not get the A-level grades you want this summer, what is your likely next step?

Take autumn exams (132)
46.32%
Take exams next summer (44)
15.44%
Change uni choice through clearing (69)
24.21%
Apply to uni next year instead (26)
9.12%
I'm not applying to university (14)
4.91%

Watched Threads

View All
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise