Question : Find the value of the following expression.
$12\left(\sin^4 heta+\cos^4 heta ight)+18\left(\sin^6 heta+\cos^6 heta ight)+78 \sin^2 heta \cos^2 heta$
Option 1: 30
Option 2: 40
Option 3: 10
Option 4: 20

Question

Question : Find the value of the following expression.
$12\left(\sin^4 heta+\cos^4 heta ight)+18\left(\sin^6 heta+\cos^6 heta ight)+78 \sin^2 heta \cos^2 heta$

Option 1: 30

Option 2: 40

Option 3: 10

Option 4: 20

Team Careers360 · Accepted Answer

Correct Answer: 30

Solution : $12(\sin^4 heta+\cos^4 heta)+18(\sin^6 heta+\cos^6 heta)+78 \sin^2 heta \cos^2 heta$
$=12[(\sin^2 heta+\cos^2 heta)^2-2\sin^2 heta \cos^2 heta]+18[(\sin^2 heta+\cos^2 heta)^3-3\sin^2 heta \cos^2 heta(\sin^2 heta+\cos^2 heta)]+78 \sin^2 heta \cos^2 heta$
$=12[1-2\sin^2 heta \cos^2 heta]+18[1-3\sin^2 heta \cos^2 heta]+78 \sin^2 heta \cos^2 heta$
$= 12-24\sin^2 heta \cos^2 heta+18-54\sin^2 heta \cos^2 heta+78 \sin^2 heta \cos^2 heta$
$= 12+18$
$=30$
Hence, the correct answer is 30.

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Question : Find the value of the following expression. 12(sin4⁡θ+cos4⁡θ)+18(sin6⁡θ+cos6⁡θ)+78sin2⁡θcos2⁡θOption 1: 30Option 2: 40Option 3: 10Option 4: 20

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Question : Find the value of the following expression.
$12 (\sin^{4} θ + \cos^{4} θ) + 18 (\sin^{6} θ + \cos^{6} θ) + 78 \sin^{2} θ \cos^{2} θ$
Option 1: 30
Option 2: 40
Option 3: 10
Option 4: 20