find x , cos^2 x -sin^2 x = (square root 3)/ 2?

Answer 1

cos^2(x) -sin^2(x) = (sqrt(3))/ 2

Use this identity:
cos^2(x) - sin^2(x) = cos(2x)

So,
cos(2x) = (sqrt(3)) / 2

let y = 2x

cos(y) = (sqrt(3)) / 2
y = ... , Pi/6, 11Pi/6, 13Pi/6, 23Pi/6, ...

2x = ... , Pi/6, 11Pi/6, 13Pi/6, 23Pi/6, ...
x = ... , Pi/12, 11Pi/12, 13Pi/12, 23Pi/12, ...

Answer 2

cos 2x = √3 / 2
2x = (30° ± k 360°) , (330° ± k 360°) ; k = 1 , 2 , 3 -----
x = 15°± k 180° , 165° ± k 180°; k = 1, 2 , 3 --

Answer 3

From trigo identity, cos^2 (A) -sin^2 (A) = cos (2A)

cos^2 x -sin^2 x = Sqrt(3)/ 2
cos4x = sqrt(3)/2

4x = 30 or 330
x = 7.5 or 82.5 degree

or you may use Pi

4x = Pi/6 or 11Pi/6

Answer 4

cos2x=sqrt(3)/2
so 2x= pi/6 +2kpi
and 2x = 11pi/6+2kpi
so x= pi/12 +kpi and x= 11pi/12+kpi
If you look for solutions 0<=x<=2pi
x=pi/12,x=13pi/12,x=11pi/12 and x=23pi/12

Answer 5

Beef and Bean Burritos
1 lb. ground chuck

1 onion chopped

4 large garlic cloves minced

3 T. cumin

2 15 oz. cans pinto beans rinsed and drained

1 14 .5 oz. can beef broth

1 4 oz. can chopped green chilies

4 green onions sliced

Heat large skillet over medium high heat. Add ground beef and cook until brown. Add chopped onion and garlic, cook another 5 minutes. Stir in cumin and cook 1 minute. Add beans, broth and chilies and cook until beans are creamy and thickened, crushing beans with the back of a spoon, about 20 minutes Mix in green onions.

Transfer beans and beef mixture to a serving dish. Serve with tortillas, cheese, sour cream and salsa or Pico de Gallo.

Answer 6

substitute sin^2x with 1 - cos^2x (through the identity) and you get;

2cos^2x = sqrt3/2 + 1

then you can work it out from there.