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Multiplication with Vectors

Eliminate θ...

Question

Eliminate $θ$ and find a relation in x, y, a and b for the following question.
If $x = a s e c θ$ and $y = a t a n θ$ , find the value of $x^{2} - y^{2}$ .

A

x^{2} y^{2} = a^{2}

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B

x^{2} + y^{2} = a^{2}

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C

x^{2} - y^{2} = a^{2}

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D

x^{2} = a^{2} y^{2}

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Solution

The correct option is C $x^{2} - y^{2} = a^{2}$
$x^{2} - y^{2} = a^{2} {sec}^{2} θ - a^{2} {tan}^{2} θ = a^{2} ({sec}^{2} θ - {tan}^{2} θ) = a^{2}$ .

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