If sinA + sin² A = 1, then the value of the expression (cos² A + cos⁴ A) is
a. 1
b. 1/2
c. 2
d. 3

Solution:

Given, sinA + sin² A = 1

It can be written as

sin A = 1 - sin² A …. (1)

We have to find the value of (cos² A + cos⁴ A)

Using the trigonometric identities,

cos² A = 1 - sin² A ….. (2)

From both the equations

sin A = cos² A

Now, (cos² A + cos⁴ A) = (cos²A + (sin A)²)

= cos²A + sin²A

Using the trigonometric identities,

cos² A + sin² A = 1

Therefore, (cos² A + cos⁴ A) = 1

✦ Try This: If cosA + cos² A = 1, then the value of the expression (cos A/sin²A) is

Given, cosA + cos² A = 1

It can be written as

cos A = 1 - cos² A ….. (1)

We have to find the value of the expression (cos A/sin²A)

Using the trigonometric identities,

sin² A = 1 - cos² A …. (2)

From both the equations

cos A = sin² A

Now, cos A/sin²A = sin²A/sin²A

= 1

Therefore, the value of the expression (cos A/sin²A) is 1.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8

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NCERT Exemplar Class 10 Maths Exercise 8.1 Problem 9

If sinA + sin² A = 1, then the value of the expression (cos² A + cos⁴ A) is a. 1, b. 1/2, c. 2, d. 3

Summary:

If sinA + sin² A = 1, then the value of the expression (cos² A + cos⁴ A) is 1

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