Question

find cos2a and tan2a if sina= root 3/2, A lies in 2nd quadrant

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

$cos2a=-\frac{1}{2}$

$tan2a=\sqrt{3\\}$

Step-by-step explanation:

$sina=\frac{\sqrt{3} }{2} \\therefore, a = 120$

Becuz a lies in 2nd quadrant

Now,

$sin2a = 2sina*cosa$

$=2*sin(120)*cos(120) \\= 2*\frac{\sqrt{3} }{2}*-\frac{1}{2} \\= -\frac{\sqrt{3} }{2}$

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$cos2a=(cosa)^{2} - (sina)^{2}\\= (-\frac{1}{2} )^{2} - (\frac{\sqrt{3} }{2} )^{2}\\= \frac{1}{4} - \frac{3}{4} \\= - \frac{1}{2} (Ans)$

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$tan2a= \frac{sin2a}{cos2a} \\=\frac{-\frac{\sqrt{3} }{2} }{-\frac{1}{2} } \\=\sqrt{3 } (Ans)$