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Question 53
If $$\cos x = \frac{-1}{2} and \pi < x < \frac{3\pi}{2}$$, then the value of $$4 \tan^2 x + 3 \cosec^2 x$$ is:
Solution
cos x =-0.5
Now x is between $$\pi\ \ and\ \frac{3\pi\ }{2}$$
we know cos$$\frac{4\pi\ }{3}=-\frac{1}{2}$$
so x =Â $$\frac{4\pi\ }{3}$$
Now 4$$\tan^2\ \frac{4}{3}\pi\ +3\operatorname{cosec}^2\ \frac{4\pi\ }{3}$$
we get 4(3) +3(4/3) = 12+4 =16
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