Find dy/dx: sin² x + cos² y = 1

Solution:

A derivative helps us to know the changing relationship between two variables. Consider the independent variable 'x' and the dependent variable 'y'.

The change in the value of the dependent variable with respect to the change in the value of the independent variable expression can be found using the derivative formula.

Given, sin² x + cos² y = 1

Let us find the derivative on both sides with respect to x.

On differentiating with respect to x, we get

⇒ d/dx ( sin² x + cos² y) = d/dx (1)

⇒ d/dx ( sin² x) + d/dx (cos² y) = 0

Since derivative of constant function is zero.

Hence,

⇒ 2 sin x cos x + 2 cos y ( - sin y ) dy / dx = 0

Using trigonometric formulaes, we can write as 

⇒ sin 2x - sin 2y dy/dx = 0

⇒ sin 2x = sin 2y dy/dx

Therefore,

dy/dx = sin 2x / sin 2y

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NCERT Solutions Class 11 Maths - Chapter 5 Exercise 5.3 Question 8

Find dy/dx: sin² x + cos² y = 1

Summary:

The derivative of  sin² x + cos² y = 1 with respect to x is dy/dx = sin 2x / sin 2y .A derivative helps us to know the changing relationship between two variables.