Question

evaluate
cot²π/6+cosec²5π/6+3tan²7π/6​

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

❥${\underline{\underline{\large{\mathtt{ANSWER:-}}}}}$

8

❥${\underline{\underline{\large{\mathtt{SOLUTION:-}}}}}$

${cot}^{2} \frac{\pi}{6} + {cosec}^{2} \frac{5\pi}{6} + 3 {tan}^{2} \frac{7\pi}{6} \\ = {cot}^{2} \frac{180}{6} + {cosec}^{2} \frac{5 \times 180}{6} + 3 {tan}^{2} \frac{7 \times 180}{6} \\ = {cot}^{2} 30 + {cosec}^{2} 150 + 3 {tan}^{2} 210 \\ = {cot}^{2} 30 + {cosec}^{2} (1 \times 90 + 60) + 3 {tan}^{2} (2 \times 90 + 30) \\ = {cot}^{2} 30 + {sec}^{2} 60 + 3 {tan}^{2} 30$

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

$=3+4+1$

$=8$

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MORE INFORMATION :

• sin(-∅) = - sin∅

• cos(-∅) = cos∅

• tan(-∅) = - tan∅

• cosec(-∅) = - cosec∅

• sec(-∅) = sec∅

• cot (-∅) = -cot∅

• If n = Even ,

• sin(n × 90±∅) =sin∅or(-sin∅)
• cos(n ×90±∅)=cos∅or(-cos∅)
• tan(n ×90±∅)=tan∅or(-tan∅)

• If n = Odd ,

• sin(n × 90±∅)=cos∅or(-cos∅)
• cos(n ×90±∅)=sin∅or(-sin∅)
• tan(n ×90±∅)=cot∅or(-cot∅)

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