Question 140
The value of $$\frac{1}{\sqrt{2}}sin\frac{\pi}{6}cos\frac{\pi}{4}-cot\frac{\pi}{3}sec\frac{\pi}{6}+\frac{5tan\frac{\pi}{4}}{12sin\frac{\pi}{2}}$$ is equal to
Solution
Expression : $$\frac{1}{\sqrt{2}}sin\frac{\pi}{6}cos\frac{\pi}{4}-cot\frac{\pi}{3}sec\frac{\pi}{6}+\frac{5tan\frac{\pi}{4}}{12sin\frac{\pi}{2}}$$
= $$\frac{1}{\sqrt{2}} (\frac{1}{2} * \frac{1}{\sqrt{2}}) - (\frac{1}{\sqrt{3}} * \frac{2}{\sqrt{3}}) + \frac{5*1}{12*1}$$
= $$(\frac{1}{\sqrt{2}} * \frac{1}{2\sqrt{2}}) - \frac{2}{3} + \frac{5}{12}$$
= $$\frac{1}{4} - \frac{1}{4}$$
= $$0$$
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