Monday

March 2, 2015

March 2, 2015

Posted by **Nikki** on Sunday, July 15, 2012 at 5:48pm.

cos^2(x) = sin^2(x/2)

- Trigonometry -
**Damon**, Sunday, July 15, 2012 at 6:00pmsin (x/2 ) = + sqrt([1-cos x]/2) if x/2 in q 1 or 2 thus if 0 < x < 2 pi

sin^2 (x/2) = [1-cos x]/2

so

cos^2 x = [1 - cos x]/2

2 cos^2 x = 1 - cos x

2 cos^2 x + cos x = 1

let z = cos x

2 z^2 + z -1 = 0

(2 z - 1)(z +1) = 0

z = cos x = 1/2

or cos x = -1

x = 60 deg (pi/3) or -60 deg (5 pi/3)

or x = 180 deg (pi)

**Answer this Question**

**Related Questions**

Trigonometry - Use the half-angle identities to find all solutions on the ...

Pre-Calc/Math - Use factoring, the quadratic formula, or identities to solve cos...

Trigonometry - Identities - If tan 2x = - 24/7, where 90 degrees < x < 180...

Math - Can I please get some help on these questions: 1. How many solutions does...

Trigonometry - Find all solutions of the equation in the interval [0,2pi] ...

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

trigonometry - Verify that following are identities: 1. cos 3t = 4 cosł t-3 cos ...

Pre-Calculus - cos^2(x) + sin(x) = 1 - Find all solutions in the interval [0, ...

Math - 1. On the interval [0, 2pi] what are the solutions to the equation ...

trig - I need to find all solutions of the given equations for the indicated ...