Question

Heya ✌

Question -
2sin (theta) + 3tan (theta) = ?



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Answer 1

Answer:

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Answer 2

2$\sin \theta$ + 3$\tan \theta$ = $\tan \theta (2\cos \theta+3)$

Step-by-step explanation:

We have,

2$\sin \theta$ + 3$\tan \theta$

To find, 2$\sin \theta$ + 3$\tan \theta$ = ?

∴ 2$\sin \theta$ + 3$\tan \theta$

Using the trigonometric identity,

$\tan A=\dfrac{\sin A}{\cos A}$

= 2$\sin \theta+$  $3\dfrac{\sin \theta}{\cos \theta}$

Taking LCM of denominator part, we get

= $\dfrac{2\sin \theta\cos \theta+3\sin \theta}{\cos \theta}$

Taking $\sin \theta$ as common in denominator, we get

= $\dfrac{\sin \theta(2\cos \theta+3)}{\cos \theta}$

= $\dfrac{\sin \theta}{\cos \theta} (2\cos \theta+3)$

= $\tan \theta (2\cos \theta+3)$

∴ 2$\sin \theta$ + 3$\tan \theta$ = $\tan \theta (2\cos \theta+3)$