If cosA + cos2 A = 1, then sin2 A + sin4 A = 1. Write ‘True’ or ‘False’ and justify your answer
Solution:
Given, cos A + cos² A = 1
We have to prove sin² A + sin⁴ A = 1
Using the trigonometric identities,
sin² A = 1 - cos² A
So, cos A = 1 - cos² A
cos A = sin² A
Now, (sin² A + sin⁴ A) = (sin²A + (cos A)²)
= sin²A + cos²A
Using the trigonometric identities,
cos² A + sin² A = 1
Therefore, the value of the expression (sin² A + sin⁴ A) is 1.
✦ Try This: If sinA + sin² A = 1, then the value of the expression (sin A/cos² A) is
Given, sinA + sin² A = 1
We have to find the value of (sin A/cos² A)
Using the trigonometric identities,
cos² A = 1 - sin² A
So, sin A = 1 - sin² A
sin A = cos² A
Now, sin A/cos² A = cos² A/cos² A
= 1
Therefore, (sin A/cos² A) = 1
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.2 Problem 5
If cosA + cos2 A = 1, then sin2 A + sin4 A = 1. Write ‘True’ or ‘False’ and justify your answer
Summary:
The sine function can be defined as the ratio of the length of the perpendicular to the length of the hypotenuse in a right angled triangle.The statement “If cosA + cos² A = 1, then sin² A + sin⁴ A = 1” is true
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