Question

If root 3 sinA =cosA,find the value of sinA.tanA.(1+cotA)+/sinA + cosA

Answer 1

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$\sqrt{3} \sin(a) = \cos(a) \\ \frac{ \ \cos(a) }{ \ \sin(a) } = \sqrt{3} \\ \cot(a) = \sqrt{3} \\ on \: comparing \\ a = 30 \\ now \: \\ \sin(a). \tan(a). \frac{(1 + \cot(a))}{ \sin(a) + \cos(a) } \\ = \sin(30). \tan(30) . \frac{1 + \cot(30) }{ \sin(30) + \cos(30) } \\ \frac{1}{2} \times \frac{1}{ \sqrt{3} } \times \frac{1 + \sqrt{3} }{ \frac{1}{2} + \frac{ \sqrt{3} }{2} } \\ = \frac{1}{2 \sqrt{3} } \times \frac{1 + \sqrt{3} }{ \frac{1 + \sqrt{3} }{2} } \\ \frac{1}{2 \sqrt{3} } \times 1 + \sqrt{3} \times \frac{2}{1 + \sqrt{3} } \\ = \frac{1}{ \sqrt{3} } \\ on \: rationalising \: we \: get \: \\ \frac{ \sqrt{3} }{3}$