Question

falue of cosec²60°-cot²60°

Answer 1

by using the identity formula:
cosec²x-cot²x=1
here,x=60°
cosec²60°-cot²60°=1
another method:
cosec²60°-cot²60°=(2/√3)²-(1/√3)²=(4-1)/3=3/3=1
your answer will be cose²60°-cot²60°=1.
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Answer 2

Given:-

Cosec² 60° - cot² 60°.

Solution:-

$\bf\ ⇒ \: (\frac{2}{ \sqrt{3} }) ^{2} \: - \: ( \frac{1}{ \sqrt{3} }) ^{2}$

$\bf\ ⇒ \: \frac{2^{2} }{( \sqrt{3}) ^{2} } \: - \: \frac{1^{2} }{( \sqrt{3})^{2} }$

$\bf\ ⇒ \frac{4}{3} \: - \: \frac{1}{3} \: = \: \frac{4 \: - \: 1}{3}$

$\bf\ ⇒ \: \frac{3}{3}$

$\bf\ ⇒ \: {\boxed{1}}$

Hence,Verified!