# Class 12 RD Sharma Solutions – Chapter 11 Differentiation – Exercise 11.7 | Set 3

• Last Updated : 20 May, 2021

### Question 21. If and , find Solution:

Here, Differentiate it with respect to t using chain rule, And, Differentiate it with respect to t using quotient rule, ### Question 22. Find , if y = 12(1 – cos t), x = 10(t – sin t), Solution:

It is given that,

y = 12(1 – cos t),

x = 10(t – sin t)

Therefore,  Therefore, ### Question 23. If x = a(θ – sin θ) and y = a(1 – cos θ), find , at θ = Solution:

Here,

x = a(θ – sin θ)

and

y = a(1 – cos θ)

Then,  Therefore, ### Question 24. If x = a sin 2t (1 + cos 2t) and y = b cos 2t (1 – cos 2t), show that at t = Solution:

Consider the given functions,

x = a sin 2t (1 + cos 2t)

and

y = b cos 2t (1 – cos 2t)

Write again the functions,

x = a sin 2t + sin 4t

Differentiate the above function with respect to t, y = b cos 2t (1 – cos 2t)

y = b cos 2t – b cos2 2t From equation (1) and (2) ### Question 25. If x = cos t (3 – 2cos2t) and y = sin t (3 – 2 sin2t), find the value of at t = Solution:

Here, the given function:

x = cos t (3 – 2cos2t)

x = cos t – 2cos3t y = sin t (3 – 2 sin2t)

y = 3cos t – 2sin3t ### Question 26. If , find Solution:

Here, and    ### Question 27. If x = 3sin t – sin3t, y = 3cos t – cos3t, find Solution:

x = 3sin t – sin3t

and,

y = 3cos t – cos3t When,  ### Question 28. If , find Solution: and,  and   My Personal Notes arrow_drop_up