Question

if secA = x+1/4x , prove that secA +tanA= 2x or 1/2x?

Answer 1

Answer on Question #45833 – Math - Trigonometry

if secA = x + 1/4x, prove that secA + tanA = 2x or 1/2x?

Solution.

$$secA = x + \frac{1}{4x} = \frac{4x^2 + 1}{4x}, \quad cosA = \frac{1}{secA} = \frac{4x}{4x^2 + 1},$$ $$sinA = \sqrt{1 - \cos^2 A} = \sqrt{1 - \left(\frac{4x}{4x^2 + 1}\right)^2} = \frac{4x^2 - 1}{4x^2 + 1}$$ $$\tan A = \frac{\sin A}{\cos A} = \frac{4x^2 - 1}{4x}$$

Thus, $secA + \tan A = \frac{4x^2 + 1}{4x} + \frac{4x^2 - 1}{4x} = 2x$ Q.E.D.

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