Question:
The general solution of the equation
\( \sin 2x + 2\sin x + 2\cos x + 1 = 0 \)
is:
The general solution of the equation
\( \sin 2x + 2\sin x + 2\cos x + 1 = 0 \)
is:
\( \sin 2x + 2\sin x + 2\cos x + 1 = 0 \)
is:
Show Hint
Convert expressions into single trigonometric functions when possible.
Updated On: Mar 23, 2026
- \(3n\pi-\dfrac{\pi}{4}\)
- \(2n\pi+\dfrac{\pi}{4}\)
- \(2n\pi+(-1)^n\sin^{-1}\!\left(\dfrac{1}{\sqrt3}\right)\)
- nπ-(π)/(4)
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The Correct Option is D
Solution and Explanation
Step 1: Rearranging:
\( 2(\sin x + \cos x) + (\sin 2x + 1) = 0 \)
Step 2: Simplifying gives:
\( \tan x = -1 \)
Step 3:
\( x = n\pi - \dfrac{\pi}{4} \)
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