Question

if sin theta = √3 by 2 then cot(90-theta)=
A) 1/2
B) √3
C) 1/√3
D) √2​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

$\displaystyle\sf{ \sin \theta = \frac{ \sqrt{3} }{2} } \: \: then \: \: \displaystyle\sf{ \cot( {90}^{ \circ} - \theta ) }$

A) 1/2

B) √3

C) 1/√3

D) √2

EVALUATION

Here it is given that

$\displaystyle\sf{ \sin \theta = \frac{ \sqrt{3} }{2} }$

$\displaystyle\sf{ \implies \: \sin \theta = \sin \: {60}^{ \circ} }$

$\displaystyle\sf{ \implies \: \theta = \: {60}^{ \circ} }$

Now

$\displaystyle\sf{ \cot( {90}^{ \circ} - \theta ) }$

$\displaystyle\sf{ = \tan\theta }$

$\displaystyle\sf{ = \tan {60}^{ \circ} }$

$\displaystyle\sf{ = \sqrt{3} }$

FINAL ANSWER

Hence the correct option is B) √3

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