Tuesday

July 29, 2014

July 29, 2014

Posted by **Katie** on Thursday, April 23, 2009 at 7:17pm.

Solve: sin(3x)-sin(x)=cos(2x)

so far i've gotten to:

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

Where would I go from here?

- Math -
**Reiny**, Friday, April 24, 2009 at 12:49amyou cannot do that!

looks like you factored

sin(3x) - sinx = sinx(sin(2x) - 1)

not true!!!!!!

then sin 90 - sin 30 = sin30(sin60 - 1) Is it???, of course not

we have a formula for sin (3x)

= 3(cos^2 x)(sinx) - sin^3 x

then

sin(3x)-sin(x)=cos(2x)

3(cos^2 x)(sinx) - sin^3 x = 1 - 2sin^2 x

replace cos^2 x with 1 - sin^2x, expand and simplify to get

-4sin^3 x + 2sin^2 x + 2sinx - 1 = 0

2sin^2x(-2sinx + 1) -1(-2sinx + 1) = 0

(-2sinx + 1)(2sin^2x - 1) = 0

sinx = 1/2 or sinx = ± 1/√2

x = 30, 150, 45, 135 degrees

**Related Questions**

tigonometry - expres the following as sums and differences of sines or cosines ...

Math, Pre-Calc - the original problem was: Solve: sin(3x)-sin(x)=cos(2x) so far ...

TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...

algebra - Can someone please help me do this problem? That would be great! ...

Precal - I do not understand how to do this problem ((sin^3 A + cos^3 A)/(sin A...

Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...

Math - Calculus - The identity below is significant because it relates 3 ...

trig - Reduce the following to the sine or cosine of one angle: (i) sin145*cos75...

calculus - Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x...

Calc. - Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln...