Question : If $2 \sin heta+2 \sin ^2 heta=2$, then the value of $2 \cos ^4 heta+2 \cos ^2 heta$ is:
Option 1: 4
Option 2: 2
Option 3: 1
Option 4: 0

Question

Question : If $2 \sin heta+2 \sin ^2 heta=2$, then the value of $2 \cos ^4 heta+2 \cos ^2 heta$ is:

Option 1: 4

Option 2: 2

Option 3: 1

Option 4: 0

Team Careers360 · Accepted Answer

Correct Answer: 2

Solution : Given: $2 \sin heta+2 \sin ^2 heta=2$
⇒ $2\sin heta + 2\sin^2 heta = 2(\sin^2 heta + \cos^2 heta)$
⇒ $2\sin heta + 2\sin^2 heta = 2\sin^2 heta + 2\cos^2 heta$
⇒ $2\sin heta = 2\cos^2 heta$
⇒ $\sin heta = \cos^2 heta$
Putting the value in the given equation,
$2 \cos ^4 heta+2 \cos ^2 heta$
$=2\sin^2 heta + 2\sin heta = 2$
Hence, the correct answer is 2.

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Question : If 2sin⁡θ+2sin2⁡θ=2, then the value of 2cos4⁡θ+2cos2⁡θ is:Option 1: 4Option 2: 2Option 3: 1Option 4: 0

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Question : If $2 \sin θ + 2 \sin^{2} θ = 2$ , then the value of $2 \cos^{4} θ + 2 \cos^{2} θ$ is:
Option 1: 4
Option 2: 2
Option 3: 1
Option 4: 0