The value of 6 ( sin 6 + cos 6 ) - 9 ( sin 4 + cos 4 ) + 4 is

Question

The value of $6 (\sin^{6} θ + \cos^{6} θ) - 9 (\sin^{4} θ + \cos^{4} θ) + 4$ is

Smart Achievers · Accepted Answer

(1)

$6 (\sin^{6} θ + \cos^{6} θ) - 9 (\sin^{4} θ + \cos^{4} θ) + 4$

$= 6 [{(\sin^{2} θ + \cos^{2} θ)}^{3} - 3 \sin^{2} θ \cos^{2} θ (\sin^{2} θ + \cos^{2} θ)] - 9 [{(\sin^{2} θ + \cos^{2} θ)}^{2} - 2 \sin^{2} θ \cos^{2} θ] + 4$

$= 6 [1 - 3 \sin^{2} θ \cos^{2} θ] - 9 (1 - 2 \sin^{2} θ \cos^{2} θ) + 4$

$= 6 - 9 + 4 = 1$

Solution

Q.
The value of $6 (\sin^{6} θ + \cos^{6} θ) - 9 (\sin^{4} θ + \cos^{4} θ) + 4$ is

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Solution

Q. The value of 6(sin6θ+cos6θ)-9(sin4θ+cos4θ)+4 is

Ans. (1) 6(sin6θ+cos6θ)-9(sin4θ+cos4θ)+4 =6[(sin2θ+cos2θ)3-3sin2θcos2θ(sin2θ+cos2θ)]-9[(sin2θ+cos2θ)2-2sin2θcos2θ]+4 =6[1-3sin2θcos2θ]-9(1-2sin2θcos2θ)+4 =6-9+4=1

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Q.
The value of $6 (\sin^{6} θ + \cos^{6} θ) - 9 (\sin^{4} θ + \cos^{4} θ) + 4$ is