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

x = n π

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x = \frac{n π}{3}

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x = \frac{n π}{4}

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x = \frac{n π}{2}

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Solution

The correct option is A $x = n π$
${cos}^{50} x - {sin}^{50} x = 1$ or ${cos}^{50} x = 1 + {sin}^{50} x$
L.H.S. $\leq 1$ and R.H.S. $\geq 1$
Hence, we must have ${cos}^{50} x = 1 + {sin}^{50} x = 1$ or $sin x = 0$ or $x = n π$

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Solve cos50x−sin50x=1

The correct option is A x=nπcos50x−sin50x=1 or cos50x=1+sin50xL.H.S.≤1 and R.H.S.≥1Hence, we must have cos50x=1+sin50x=1 or sinx=0 or x=nπ

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

The correct option is A $x = n π$
${cos}^{50} x - {sin}^{50} x = 1$ or ${cos}^{50} x = 1 + {sin}^{50} x$
L.H.S. $\leq 1$ and R.H.S. $\geq 1$
Hence, we must have ${cos}^{50} x = 1 + {sin}^{50} x = 1$ or $sin x = 0$ or $x = n π$