Prove that-2-6-cosec5 -6-3 tan 2 -6-6

We have L.H.S = cot^2 π/6+ cosec5π/6 + 3 tan^2 π/6= 6 Now cosec 5π/6 = cosec (π π/6 ) = cosec π/6 = 2 ∴cot^2 π/6+ cosec5π/6+3 tan^2 π/6 = (√(3))^2 +2+3 × ( 1/√ ...

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Standard XI

Mathematics

Basic Trigonometric Identities

Prove that:2π...

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

We have

L.H.S = ${cot}^{2} \frac{π}{6} + cosec \frac{5 π}{6} + 3 {tan}^{2} \frac{π}{6}$ = 6

Now cosec $\frac{5 π}{6}$ = cosec $(π - \frac{π}{6})$ = cosec $\frac{π}{6}$ = 2

$∴ {cot}^{2} \frac{π}{6} + cosec \frac{5 π}{6} + 3 {tan}^{2} \frac{π}{6}$

= $(\sqrt{3})^{2} + 2 + 3 \times {(\frac{1}{\sqrt{3}})}^{2}$

= 3+2+3 $\times \frac{1}{3}$

= 5+1 = 6 = R.H.S

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Similar questions

Q. Prove that:

{cot}^{2} \frac{π}{6} + cosec \frac{5 π}{6} + 3 {tan}^{2} \frac{π}{6} = 6

Q. Prove that:

c o t^{2} \frac{π}{6} + c o s e c \frac{5 π}{6} + 3 t a n^{2} \frac{π}{6} = 6

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{cot}^{2} \frac{π}{6} + {cosec}^{2} \frac{5 π}{6} + 3 {tan}^{2} \frac{π}{6} = 8

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is equal to :

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_________

\infty = 6

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Prove that: cot2π6+cosec5π6+3tan2π6=6

We have L.H.S = cot2π6+cosec5π6+3tan2π6= 6 Now cosec 5π6 = cosec (π−π6) = cosec π6 = 2 ∴cot2π6+cosec5π6+3tan2π6 = (√3)2+2+3×(1√3)2 = 3+2+3 ×13 = 5+1 = 6 = R.H.S

Prove that:

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