Question

Find general solution of

sin^2theta • sectheta+√3 tantheta= 0​

Answer 1

Step-by-step explanation:

We have,

$\sin^{2} ( \theta) . \sec( \theta) + \sqrt{3} \tan( \theta) = 0$

$\implies \sin ( \theta) . \sin( \theta) . \frac{1}{ \cos( \theta)} + \sqrt{3} \tan( \theta) = 0$

$\implies \sin ( \theta) . \frac{ \sin( \theta) }{ \cos( \theta)} + \sqrt{3} \tan( \theta) = 0$

$\implies \sin ( \theta) . \tan( \theta) + \sqrt{3} \tan( \theta) = 0$

$\implies \tan( \theta) \{ \sin( \theta) + \sqrt{3} \}= 0$

Either $\tan( \theta)=0$ or $\{ \sin( \theta) + \sqrt{3} \}= 0$

Since, $-1\leqslant \sin(\theta) \leqslant1$, so, $\sin(\theta) ≠ -\sqrt{3}$

Then,

$\tan( \theta)= 0$

$\implies \theta= n \pi$

Where, $n\in\:I$

Answer 2

Answer:

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