Physics, asked by sharmayukta5077, 11 months ago

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

Answers

Answered by nirman95
5

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}

#SPJ3

Answered by parulsehgal06
0

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:  

https://brainly.in/question/5488061?referrer=searchResults

         

   

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