Question

If cosx cos(pi/7) + sinx sin(pi/7) = -(sqrt(2))/2, then x can equal...? (Check all that apply) (Will give medal & fan!) A. pi/4 + pi/7 + 2npi B. 5pi/4 + pi/7 + 2npi C. 7pi/4 + pi/7 + 2npi D. 3pi/4 + pi/7 + 2npi

Answer 1

If sinxcos(π/7) - sin(π/7) cosx = - √ 2 / 2 , then x can equal: ______ Check all that apply: 1)π/4 ... Best Answer: sin ( x - ( pi / 7 ) ) = - sqrt ( 2 ) / 2

Answer 2

Options B and D

Explanation:

Given that

`cos x cos (\pi)/(7) +sinx sin (\pi)/(7) =(-√(2) )/(2)`

Use the formula for sum angles for Cos as

Cos A cos B +sin A sin B = cos (A-B)

we have

`cos (x-(\pi)/(7) ) = (-√(2) )/(2)`

First let us solve principal solution

cos negative in the II quadrant

Hence principal soluton is
`\pi-(\pi)/(4) =(3\pi)/(4)`+
`(\pi)/(7)`

Again it is negative in third quadrant i.e. x =
`(5\pi)/(4)`+
`(\pi)/(7)`

General solution is
`(5\pi)/(4)`+
`(\pi)/(7)+2n\pi and\\\\(3\pi)/(4)`+
`(\pi)/(7)+2n\pi`

Options B and D