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Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

Prove that: 2...

Question

Prove that: ${cot}^{2} \frac{π}{6} + cosec \frac{5 π}{6} + 3 {tan}^{2} \frac{π}{6} = 6$

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Solution

L.H.S $= {cot}^{2} \frac{π}{6} + cosec \frac{5 π}{6} + 3 {tan}^{2} \frac{π}{6}$
$= {cot}^{2} \frac{π}{6} + cossec (π - \frac{π}{6}) + 3 {tan}^{2} \frac{π}{6}$
$= {cot}^{2} \frac{π}{6} + cossec \frac{π}{6} + 3 {tan}^{2} \frac{π}{6}$
$= (\sqrt{3})^{2} + 2 + 3 {(\frac{1}{\sqrt{3}})}^{2}$
$= 3 + 2 + 1$
$= 6 =$ R.H.S
So, L.H.S. = R.H.S.
${cot}^{2} \frac{π}{6} + cosec \frac{5 π}{6} + 3 {tan}^{2} \frac{π}{6} = 6$
Hence proved.

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Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

Standard XII Mathematics

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