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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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