Question

if y= 2sin^2 theta + tan theta then dy/dtheta will be what

Answer 1

Given:

$y = 2 { \sin}^{2}( \theta) + \tan( \theta)$

To find:

Value of $dy/d\theta$ ?

Calculation:

$y = 2 { \sin}^{2}( \theta) + \tan( \theta)$

$\implies\dfrac{dy}{d \theta} = 2 \dfrac{d \{{ \sin}^{2}( \theta) \}}{ d\theta} + \dfrac{d \{\tan( \theta) \} }{d \theta}$

• Applying Chain Rule of differentiation:

$\implies\dfrac{dy}{d \theta} = 2 \dfrac{d \{{ \sin}^{2}(\theta) \}}{ d \sin(\theta)} \times \dfrac{d \sin( \theta) }{d \theta} + { \sec }^{2} \theta$

$\implies\dfrac{dy}{d \theta} = 2 \{2 \sin( \theta) \cos( \theta) \} + { \sec }^{2} \theta$

$\boxed{ \implies\dfrac{dy}{d \theta} =2 \sin( 2\theta) + { \sec }^{2} \theta}$

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Answer 2

Answer:

For  $y = 2sin^{2}\theta +tan\theta$, the value of  $\frac{dy}{d\theta} = 2sin2\theta+sec^{2}\theta$

Explanation:

Differentiation:

    The derivative of a dependent variable w.r.t an independent variable is known as Differentiation.

 Given $y = 2sin^{2}\theta +tan\theta$

        differentiate the above equation w.r.t θ

          $\frac{dy}{d\theta}=2\frac{d(sin^{2}\theta)}{d\theta}+\frac{d(tan\theta)}{d\theta}$

         $\frac{dy}{d\theta} =2{(2sin\theta cos\theta)}+{(sec^{2} \theta)}$

         $\frac{dy}{d\theta} =2{(sin2\theta)}+{(sec^{2} \theta)}$         Since, $sin2\theta=2sin\theta cos\theta$

  Hence,  $\frac{dy}{d\theta} =2{(sin2\theta)}+{(sec^{2} \theta)}$

 

    Know more about Trigonometry:  

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