Question

please help ..........................​

Answer 1

Step-by-step explanation:

cotA= 1/√3

A= 60°

substituting

1-(1/2)^2/2-(√3/2)^2

(3/4)/5/4

3/5

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Answer 2

Step-by-step explanation:

Given

$\cot( a) = \frac{1}{ \sqrt{3} }$

as we know that

$\cot(a) = \frac{b}{p} \\ therefore \: p = x\sqrt{3} \\ and \: \: b = x \\ by \: pgt \: \\ {h}^{2} = {p}^{2} + {b}^{2} \\ \: \: \: \: \: \:= {(x \sqrt{3} )}^{2} + {(x)}^{2} \\ \: \: \: \: = 3 {x}^{2} + {x}^{2} \\ \: \: \: \: {h}^{2} = 4 {x}^{2} \\ h = 2x \\ as \: we \: know \: that \\ \sin(a) = \frac{p}{h} = \frac{ \sqrt{3} }{2} \\ and \: \cos(a) = \frac{b}{h} = \frac{1}{2} \\ therefore \: \\ \frac{1 - { \cos(a) }^{2} }{2 - { \sin(a) }^{2} } = \frac{3}{5}$

$on \: taking \: lhs \\ = \frac{1 - { \cos(a) }^{2} }{2 - \sin(a) } \\ = \frac{1 - { (\frac{1}{2}) }^{2} }{2 - {( \frac{ \sqrt{3} }{2} )}^{2} }$

$= \frac{1 - \frac{1}{4} }{2 - \frac{3}{4} } \\ = \frac{ \frac{4 - 1}{4} }{ \frac{8 - 3}{4} } \\ = \frac{ \frac{3}{4} }{ \frac{5}{4} } \\ = \frac{3}{5} \\ hence \: proved$