Question

Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are ______.

पर्याय

• `(7π)/9, (11π)/8`

• `(9π)/8, (13π)/8`

• `(11π)/8, (15π)/8`

• `(15π)/8, (19π)/8`

Answer 1

Principal solutions at the equation sin 2x + cos 2x = 0, where π < x < 2 π are `underlinebb((11π)/8, (15π)/8)`.

Explanation:

The given equation is sin 2x + cos 2x = 0

`\implies` sin 2x = – cos 2x

`\implies` tan 2x = – 1 ...[∵ π < x < 2π `\implies` 2π < 2x < 4π]

`\implies` 2x = `2π + (3π)/4, 2π + ((3π)/2 + π/4)` 

`\implies` 2x = `(11π)/8, (15π)/4`

`\implies` x = `(11π)/8, (15π)/8`