If tan $(90^\circ – A)= \sqrt 3$ , What is sin A ?

If tan $(90^\circ – A)= \surd 3$ , What is sin A ?
यदि $tan(90^\circ – A)= \surd 3$, तो sin A क्या है?

$\frac{1}{2} $ $\frac{\sqrt{3}}{2}$ $\frac{\sqrt{2}}{2}$ $\frac{3}{4}$

Detailed Solution & Logic

Correct Answer:

$\frac{1}{2} $

$ \tan(90^\circ-A)=\cot A $

$ \cot A=\sqrt{3} $

$ \therefore \tan A=\frac{1}{\sqrt{3}} $

$ \tan 30^\circ=\frac{1}{\sqrt{3}} \Rightarrow A=30^\circ $

$ \therefore \sin A=\sin 30^\circ=\frac{1}{2} $

$ \frac{1}{2} $

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