Question

Value of tan square 30 degree + 2 cot square 60 degree

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Required value is 1.

Step-by-step explanation:

Given,

${tan}^{2} {30}^{o} + 2 {cot}^{2} {60}^{o} .......(1)$

We know,

$\tan( {0}^{o} ) = 0 \\ \tan( {30}^{0} ) = \frac{1}{ \sqrt{3} } \\ \tan( {45}^{o} ) = 1 \\ \tan( {60}^{o} ) = \sqrt{3} \\ \tan( {90}^{o} ) = 1$

And

$\cot( {0}^{o} ) = 0 \\ \cot( {30}^{o} ) = \sqrt{3} \\ \cot( {45}^{o} ) = 1 \\ \ \cot( {60}^{o} ) = \frac{1}{ \sqrt{3} } \\ \cot( {90}^{o} ) = 1$

From (1),

${tan}^{2} {30}^{o} + {cot}^{2} {60}^{o} .......(1)$

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

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

Required value is 1