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The value of (cos^4theta + cos^2theta sin^2 theta + sin^2 theta)/(cos^2 theta + cos^2 theta sin^2 theta + sin^4 theta) is ______.

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Question

The value of `(cos^4theta + cos^2theta sin^2 theta + sin^2 theta)/(cos^2 theta + cos^2 theta sin^2 theta + sin^4 theta)` is ______.

Fill in the Blanks
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Solution

The value of `(cos^4theta + cos^2theta sin^2 theta + sin^2 theta)/(cos^2 theta + cos^2 theta sin^2 theta + sin^4 theta)` is 1.

Explanation:

Let c = cos θ and s = sin θ. 

Using s2 = 1 – c2, 

Numerator = c4 + c2 s2 + s2

= c4 + c2(1 – c2) + (1 – c2) 

= 1

Denominator = c2 + c2 s2 + s4

= (1 – s2) + (1 – s2)s2 + s4 

= 1

Therefore the ratio = `1/1` = 1.

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Chapter 11: Trigonometric Identities - FILL IN THE BLANK TYPE QUESTIONS (FBQs) [Page 11.44]

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R.D. Sharma Mathematics [English] Class 10
Chapter 11 Trigonometric Identities
FILL IN THE BLANK TYPE QUESTIONS (FBQs) | Q 7. | Page 11.44
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