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# Class 12 RD Sharma Solutions – Chapter 11 Differentiation – Exercise 11.7 | Set 2

• Last Updated : 20 May, 2021

### Question 11. Find , when and Solution:

Here, Differentiating it with respect to t using quotient rule, and, Differentiating it with respect to t using quotient rule, Dividing equation (2) by (1) ### Question 12. Find , when and Solution:

Here, Differentiating it with respect to t using chain rule, Now, Differentiating it with respect to t using chain rule, Dividing equation (2) by (1) ### Question 13. Find , when and Solution:

Here, Differentiating it with respect to t using quotient rule, and, Differentiating it with respect to t using quotient rule, ### Question 14. If x = 2cosθ – cos2θ and y = 2sinθ – sin2θ, prove that Solution:

Here,

x = 2cosθ – cos2θ

Differentiating it with respect to θ using chain rule, and,

y = 2sinθ – sin2θ

Differentiating it with respect to θ using chain rule, Dividing equation (2) by equation (1), ### Question 15. If x = ecos2t and y = esin2t prove that, Solution:

Here,

x = ecos2t

Differentiating it with respect to t using chain rule, and,

y = esin2t

Differentiating it with respect to t using chain rule, Dividing equation (2) by (1)  ### Question 16. If x = cos t and y = sin t, prove that Solution:

Here,

x = cos t

Differentiating it with respect to t, and,

y = sin t

Differentiating it with respect to t, Dividing equation (2) by (1), ### Question 17. If and , Prove that Solution:

Here, Differentiating it with respect to t, and, Differentiating it with respect to t, Dividing equation (2) by (1) ### Question 18. If and , -1 < 1 < 1, prove that Solution:

Here, Put t = tan θ Differentiating it with respect to t, Further, Put t = tan θ Differentiating it with respect to t, Dividing equation (2) by (1), ### Question 19. If x and y are connected parametrically by the equation, without eliminating the parameter, find , when: , Solution:

Here, the given equations are and Thus, Therefore, ### Question 20. If and , find Solution:

Here, Differentiating it with respect to t using chain rule, And, Differentiating it with respect to t using chain rule, Dividing equation (2) by (1) My Personal Notes arrow_drop_up