Question

Pls help as soon as possible

Answer 1

Answer : A and D

Given,

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

we know the identity

cos(x)cos(y) + sin(x) sin(y) = cos(x - y)

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

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

(x -
`(\pi)/(7)`) =
`cos^(-1) ( -(√(2))/(2) )`

We know that ,

`cos^(-1) ( -(√(2))/(2) )` is
`(3\pi)/(4) and (5\pi)/(4)`

x -
`(\pi)/(7)` =
`(3\pi)/(4)` +
`2n\pi`

So x =
`(3\pi)/(4)` +
`(\pi)/(7)` +
`2n\pi`

x -
`(\pi)/(7)` =
`(5\pi)/(4)` +
`2n\pi`

So x =
`(5\pi)/(4)` +
`(\pi)/(7)` +
`2n\pi`

So answer is option A and D