Trigonometry Practice Test 1

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Question : 29 of 40

Marks: +1, -0

If

{\tan θ=p/q},

then what is

{p\secθ-q\cosecθ}/{p\secθ+q\cosecθ}

Equal to?

${p-q}/{p+q}$
${q^2-p^2}/{q^2+p^2}$
${p^2-q^2}/{q^2+p^2}$
1
None of these

Solution:

Given

{\tan θ=p/q},

⇒\secθ=√{p^2+q^2}/q

and

\cosecθ=√{p^2+q^2}/p

∴{p\secθ-q\cosecθ}/{p\secθ+q\cosecθ}

={p (√{p^2+q^2}/q)-q (√{p^2+q^2}/p)}/{p (√{p^2+q^2}/q)+q (√{p^2+q^2}/p)}

={p/q-q/p}/{p/q+q/p}={p^2-q^2}/{p^2+q^2}

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