Maths / Introduction to Trigonometry / Reciprocal Trigonometric Ratios

QUESTION

If cot $\dpi{120} \fn_jvn \large cot \theta =\frac{2ab}{a^2-b^2},$  find the values if $\dpi{120} \fn_jvn \large sin\theta\;\;and\;\;cos\theta$

EXPLANATION
Explain TypeExplanation Content
Text

$\dpi{80} \fn_phv cot \theta =\frac{1ab}{a^2-b^2}=\frac{BC}{AB}$

By pythagoras theorem,

AC = ( $\dpi{80} \fn_phv a^2$ + $\dpi{80} \fn_phv b^2$)

$\dpi{80} \fn_phv sin \theta=\frac{AB}{AC}=\frac{(a^2=b^2)k}{(a^2+b^2)k}=\frac{a^2-b^2}{a^2+b^2}$

And cos $\dpi{80} \fn_phv \theta=\frac{BC}{AC}=\frac{(2ab)k}{(a^2+b^2)k}=\frac{2ab}{a^2+b^2}$

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