Thursday

November 27, 2014

November 27, 2014

Posted by **Help** on Sunday, April 1, 2012 at 1:13am.

and

Solve the equation

cos^2(2x)–sin^2(2x)= (√3 / 2).

- Trig -
**Reiny**, Sunday, April 1, 2012 at 8:01am1st one:

2sin(2x) = cosx

4sinxcosx - cosx = 0

cosx(4sinx - 1) = 0

cosx = 0 or sinx = 1/4

for cosx = 0

x = 90° or 270° OR x = π/2 or 3π/2 radians

for sinx=1/4

x = appr 14.5° or 165.5° OR appr .253 or 2.89 radians

- Trig -
**Reiny**, Sunday, April 1, 2012 at 8:10am2nd:

cos^2(2x)–sin^2(2x)= (√3 / 2)

cos (4x) = √3/2 , using cos (2A) = cos^2 A - sin^2 A

I know cos 30° = cos 330° = √3/2

so 4x = 30° or 4x = 330°

x = 7.5° or x = 82.5°

the period of cos 4x is 360/4 ° = 90°

so adding or subtracting multiples of 90 to any of the above solutions, will yield a new solution

e.g. 7.5 + 90 = 97.5°

97.5+90 = 187.5° etc

check for x = 187.5°

LS = cos^2 375° - sin^2 375°

= .9330... - .0669...

= .866025...

RS = √3/2 = .866025...

= LS

(set your calculator to Radians using the DRG key, and get the equivalent answers in radians)

**Answer this Question**

**Related Questions**

trig - 2sin(x)cos(x)+cos(x)=0 I'm looking for exact value solutions in [0, 3&#...

math (trig) - Find sin(x/2) if sin(x)= -0.4 and 3pi/2 < or equal to (x) < ...

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

Math - Solving Trig Equations - What am I doing wrong? Equation: sin2x = 2cos2x ...

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

trigonometry (please double check this) - Solve the following trig equations. ...

URGENT - Trigonometry - Identities and Proofs - Okay, today, I find myself ...

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

Math - Solving for Trig Equations - Solve the following equation for 0 less than...

Math - Solve this equation algebraically: (1-sin x)/cos x = cos x/(1+sin x) --- ...