Multiple Choice Questions on If sin Theta cos Theta 1 2 then what is sin6 Theta cos6 Theta equal to ........ for Mathematics - All Exams Preparation

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Multiple Choice Questions

If sin Theta cos Theta 1 2 then what is sin6 Theta cos6 Theta equal to ........

Quantitative Aptitude ( CCS) Trignometry
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    If sin Θ.cos Θ = 1/2, then what is sin6Θ + cos6Θ equal to?

    1

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    2

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    3

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    1/4

    Correct Answer
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    Explanation:

    sin6Θ + cos6Θ = (sin2Θ)3 + (cos2Θ)3
    = (sin2Θ + cos2Θ)(sin4Θ + cos4Θ – sin2Θcos2Θ)
    = 1 [(sin2Θ + cos2Θ)2 – 3sin2Θcos2Θ]
    = 1 – 3 × 1/4 = 1/4

    By: Amit Kumar
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