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General Solutions of (sin theta)^2 = (sin alpha)^2 , (cos theta)^2 = (cos alpha)^2 , (tan theta)^2 = (tan alpha)^2

One of the ge...

Question

One of the general solutions to the equation $4 {sin}^{4} x + {cos}^{4} x = 1$ is?

n π \pm α / 2, α = {cos}^{- 1} (1 / 5), \forall n \in I

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n π \pm α / 2, α = {cos}^{- 1} (3 / 5), \forall n \in I

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2 n π \pm α / 2, α = {cos}^{- 1} (1 / 3), \forall n \in I

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None of these

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Solution

The correct option is B $n π \pm α / 2, α = {cos}^{- 1} (3 / 5), \forall n \in I$
$4 {sin}^{4} x + {(1 - {sin}^{2} x)}^{2} = 1$
$\Rightarrow 4 {sin}^{4} x + 1 + {sin}^{4} x - 2 {sin}^{2} x = 1$
$\Rightarrow {5 sin}^{4} x - 2 {sin}^{2} x = 0$
$\Rightarrow {sin}^{2} x = 0, {sin}^{2} x = \frac{2}{5}, {cos}^{2} x = \frac{3}{5}$
$\Rightarrow x = n π \pm α / 2, α = {cos}^{- 1} (3 / 5)$

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