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MHT CET2016MathematicsTrigonometric Equations

The solution of the equation sin ⁡ 2 x + cos ⁡ 2 x = 0 , where π < x < 2 π are

Options

  1. A7 &#x03C0; 8 , 11 &#x03C0; 8
  2. B9 &#x03C0; 8 , &#x00A0; 13 &#x03C0; 8
  3. C 11 &#x03C0; 8 , &#x00A0; 15 &#x03C0; 8
  4. D15 &#x03C0; 8 , &#x00A0; 19 &#x03C0; 8

Correct answer

C.  11 &#x03C0; 8 , &#x00A0; 15 &#x03C0; 8

Step-by-step solution

Given, sin ⁡ 2 x + cos ⁡ 2 x = 0 . Multiplying by 1 2 on both side, ∴ 1 2 sin ⁡ 2 x + 1 2 cos ⁡ 2 x = 0 ⇒ sin ⁡ π 4 + 2 x = 0 ⇒ 2 x + π 4 = n π ⇒ x = 4 n - 1 π 8 ∴ x = 11 π 8 a n d 15 π 8

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