Mathematics - Trigonometric Equation Question with Solution | TestHub

MathematicsTrigonometric EquationTrigonometric EquationEasy2 minPYQ_2018

MathematicsEasysingle choice

Equation $\sin x + \cos (t + x) + \cos (t - x) = 2$ has real solution, then $\sin t$ can be

Answer:

Solution:

Given, $\sin x + \cos (t + x) + \cos (t - x) = 2$

$\Rightarrow \sin x + 2 \cos t \cdot \cos x = 2$

For real solution

$\sqrt{1 + 4 \cos^{2} t} \geq 2$

$\Rightarrow \cos^{2} t \geq \frac{3}{4}$

$\Rightarrow - \frac{1}{2} \leq \sin t \leq \frac{1}{2}$

Hence, option (a) is correct.

Stream:BITSATSubject:MathematicsTopic:Trigonometric EquationSubtopic:Trigonometric Equation

⏱ 2mℹ️ Source: PYQ_2018

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