Question

please solve this Question

Answer 1

(Instead of x I use A)

Answer: 2

Step-by-step explanation:

Given : $cos A + sec A = 2,$

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To Find : The value of $cos^{10}A + sec^{20}A$

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Solution :

⇒$cos A + sec A = 2$

⇒$cosA +\frac{1}{cosA} = 2$

⇒$\frac{cos^2A + 1}{cos A} = 1$

⇒$cos^2A + 1 = 2cosA$

⇒$cos^2A - 2cos A + 1 = 0$

⇒$(cos A - 1)^2 = 0$

⇒ $cosA - 1 = 0$

⇒ $cos A = 1$

⇒ $sec A = \frac{1}{cos A} = \frac{1}{1} = 1$

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⇒ $cos^{10}A + sec^{20}A = (1)^{10} + (1)^{20} = 1 + 1 = 2$

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Hope it Helps !!

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