If $sin θ = \frac{a^{2} - b^{2}}{a^{2} + b^{2}},$ find the values of other five trignometric ratios.

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Solution

$sin θ = \frac{a^{2} - b^{2}}{a^{2} + b^{2}}$
$cos θ = \frac{\sqrt{(a^{2} - b^{2})^{2} - (a^{2} + b^{2})^{2}}}{(a^{2} + b^{2})} = \frac{\sqrt{4 a^{2} b^{2}}}{a^{2} + b^{2}} = \frac{2 a b}{a^{2} + b^{2}}$
$tan θ = \frac{a^{2} - b^{2}}{2 a b}$
$sec θ = \frac{a^{2} + b^{2}}{2 a b}$
$c o s e c θ = \frac{a^{2} + b^{2}}{a^{2} - b^{2}}$
$cot θ = \frac{2 a b}{a^{2} - b^{2}}$

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If sin $θ = \frac{a^{2} - b^{2}}{a^{2} + b^{2}}$ , find the values of all T-ratios of $θ$

If $s i n θ = \frac{a^{2} - b^{2}}{a^{2} + b^{2}}$ , find the values of tan $θ, s e c θ$ and $c o s e c θ .$

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