Question

cos^2A+cosA=1 ; 4sin^2A+4sin^4A+2=?​

Answer 1

Answer:

$cos {}^{2} \alpha + cos \alpha = 1$

$cos {}^{2} \alpha = 1 - cos \: \alpha$

$1 - sin {}^{2} \alpha = 1 - cos \: \alpha$

$cos \: \alpha = sin {}^{2} \alpha ......(i)$

Now we have to find,

$4sin {}^{2} \alpha + 4sin {}^{4} \alpha + 2 =$

Using eq. (i) ,

$4 \cos( \alpha ) + 4 \cos {}^{2} ( \alpha ) + 2 = 4( \cos \alpha + \cos {}^{2} \alpha ) + 2 \: .......(ii)$

From given question, replacing the value in eq. (ii)

$4(1) + 2 = 6 \: \: ans.$

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