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If sec A= x+{1}{4x} then prove that sec A + tan A = 2x or {1}{

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If $sec A = x + \frac{1}{4 x}$ then prove that $sec A + t an A = 2 x or \frac{1}{2 x}$

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If

sec A = x + \frac{1}{4 x}

then prove that

sec A + t an A = 2 x or \frac{1}{2 x}

11 mins ago

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11 mins ago

Text solutionVerified

Let,

sec A + t an A = y

..............1

Then,

= se c^{2} A - t a n^{2} A = 1

= (sec A - t an A) (sec A + t an A) = 1

= y (sec A - t an A) = 1

= sec A - t an A = \frac{1}{y}

....................2

Adding eq. 1 and eq. 2,we get

= 2 sec A = y + \frac{1}{y}

= 2 (x + \frac{1}{4 x}) = y + \frac{1}{y}

= 2 x + \frac{1}{2 x} = y + \frac{1}{y}

= y = 2 x

or

y = \frac{1}{2 x}

(on comparing two sides )

sec A + t an A = 2 x, \frac{1}{2 x}

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Question Text	If $sec A = x + \frac{1}{4 x}$ then prove that $sec A + t an A = 2 x or \frac{1}{2 x}$
Answer Type	Text solution:1
Upvotes	150