Class 12 RD Sharma Solutions – Chapter 11 Differentiation – Exercise 11.7 | Set 2
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. Ifand , Prove that
Solution:
Here,
Differentiating it with respect to t,
and,
Differentiating it with respect to t,
Dividing equation (2) by (1)
Question 18. Ifand, -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 areand
Thus,
Therefore,
Question 20. Ifand, 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)
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