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General Solution of Trigonometric Equation

The equation ...

Question

The equation $sin 2 x + cos 2 x + sin x + cos x + 1 = 0$ has no solution in:

first quadrant

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second quadrant

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third quadrant.

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fourth quadrant.

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Solution

The correct option is A first quadrant
Given Equation is $sin 2 x + cos 2 x + sin x + cos x + 1 = 0$

The terms at left hand side are all Positive in First Quadrant

All Positive terms cannot add up to give $0$

So the equation has no root in first Quadrant.

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