Question

If 4x = sec thita and 4/x = tan thita, then find the value of 16(x^2- 1/x^2 ).

Answer 1

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If 4x = sec thita and 4/x = tan thita, then find the value of 16(x^2- 1/x^2).

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Given,

Here,

4x= sec theta. -(1)

$\bold{\frac{4}{x}=sec\;theta.\;\;\;-(2)}$

Use trigonometric identity ,

sec² theta - tan² theta=1.

$\implies\bold{(4x)²-(\frac{4}{x})²=1\;from\;1\;and\;2}$

$\implies\bold{(16)²-(\frac{16}{x})²=1}$

$\implies\huge{(16)²-(\frac{1}{x})²=1}$

$\downarrow\huge{AnsweR}$

$\huge\orange{(16)²-(\frac{1}{x})²=1}$