Solve ${cos}^{50} x - {sin}^{50} x = 1$ .

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Solution

Given that ${cos}^{50} x - {sin}^{50} x = 1$

$\Rightarrow {cos}^{50} x = 1 + {sin}^{50} x$

We know that ${sin}^{50} x$ is always positive.

But maximumm value of ${cos}^{50} x$ is $1$

Therefore, $\Rightarrow {sin}^{50} x = 0$

$\Rightarrow sin x = 0$

$\Rightarrow x = n π$

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Solve cos50x−sin50x=1.

Given that cos50x−sin50x=1 ⇒cos50x=1+sin50xWe know that sin50x is always positive.But maximumm value of cos50x is 1Therefore, ⇒sin50x=0⇒sinx=0⇒x=nπ

Solve ${cos}^{50} x - {sin}^{50} x = 1$ .

Given that ${cos}^{50} x - {sin}^{50} x = 1$

$\Rightarrow {cos}^{50} x = 1 + {sin}^{50} x$

We know that ${sin}^{50} x$ is always positive.

But maximumm value of ${cos}^{50} x$ is $1$

Therefore, $\Rightarrow {sin}^{50} x = 0$

$\Rightarrow sin x = 0$

$\Rightarrow x = n π$