# 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 = 2co**sθ – 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 = e**^{cos2t} and y = e^{sin2t} prove that,

^{cos2t}and y = e

^{sin2t}prove that,

**Solution:**

Here,

x = e

^{cos2t}Differentiating it with respect to t using chain rule,

and,

y = e

^{sin2t}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 areand

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)