Question 66

What is the value of $$\cosec^2 30^\circ + \sin^2 45^\circ + \sec^2 60^\circ + \tan^2 30^\circ$$ ?

Solution

$$\cosec^2 30^\circ + \sin^2 45^\circ + \sec^2 60^\circ + \tan^2 30^\circ$$

Put the values of trigonometrical functions

$$2^2+\frac{1}{\left(\sqrt{\ 2}\right)^2}+2^2+\frac{1}{\left(\sqrt{\ 3}\right)^2}$$

$$4+\frac{1}{2}+4+\frac{1}{3}=\frac{53}{6}$$

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