If m tan(θ-30)=n tan(θ+120), thenm+n2(m-n) is equal to:
a)tan2θ
b)cos2θ
c)sin2θ
d)cot2θ
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1 Answers
11Ans) \frac{m}{n} = \frac{tan\ (\theta +120)}{tan(\theta -30)} = \frac{cos(\theta +30)cos(\theta -30)}{sin(\theta +30)sin(\theta -30)}
Therefore, \frac{m}{n} = \frac{cos^{2}\ 30 - sin^{2}\theta }{sin^{2}\ 30 - sin^{2}\theta} = \frac{3/4 -sin^{2}\theta }{1/4 - sin^{2}\theta}
On applying componendo and dividendo, we get
\frac{m+n}{m-n} = \frac{1-2\ sin^{2}\theta }{(1/2)} = 2\ cos\ 2\theta
Therefore, (b) option