Question

If xcos 45° sin 120° + sin 60° = – xsin 90° + 1 , then the value of x is:

विकल्प

• `(2sqrt(2) - sqrt(6))/(2sqrt(2) + sqrt(3))`

• `((2 - sqrt(3)))/(sqrt(2) + sqrt(3))`

• `((2 - sqrt(3)))/((2sqrt(2) + sqrt(3))`

• `((2 + sqrt(3)))/((sqrt(2) + sqrt(3))`

Answer 1

`(2sqrt(2) - sqrt(6))/(2sqrt(2) + sqrt(3))`

Explanation:

If xcos 45° sin 120° + sin 60° = – xsin 90 + 1

⇒ `x xx 1/sqrt(2) xx sin (90 + 30) + sqrt(3)/2 = - x xx 1 + 1`

⇒ `x xx 1/sqrt(2) xx cos 30 + sqrt(3)/2 = - x + 1`

⇒ `x xx 1/sqrt(2) xx sqrt(3)/2 + sqrt(3)/2 = - x + 1`

⇒ `sqrt(3)/(2 - sqrt(2)) x + x = 1 - sqrt(3)/2`

⇒ `x((sqrt(3) + 2sqrt(2))/(2sqrt(2))) = ((2 - sqrt(3))/2)`

⇒ `x = ((2 - sqrt(3)) xx 2sqrt(2))/(2(sqrt(3) + 2sqrt(2))) = ((2 - sqrt(3)) xx sqrt(2))/((sqrt(3) + 2sqrt(2))) = ((2sqrt(2) - sqrt(6)))/((2sqrt(2) + sqrt(3))`