If π=180°, find the value of tan π/2.sin π/6 + sin π/4.cos π/2 + cos π/2.sin π/3 | Values of Trigonometric Ratios

Question: If $\pi = 180°$, find the value of $tan \frac{\pi}{3}.sin\frac{\pi}{6} + sin\frac{\pi}{4}.cos\frac{\pi}{2} + cos\frac{\pi}{2}.sin\frac{\pi}{3}$.

Answer: $\dfrac{\sqrt{3}}{2}$

Solution:

Given,

$\pi = 180°$

Now,

$= tan \frac{\pi}{3}.sin\frac{\pi}{6} + sin\frac{\pi}{4}.cos\frac{\pi}{2} + cos\frac{\pi}{2}.sin\frac{\pi}{3}$

$= tan \frac{180°}{3}.sin\frac{180°}{6} + sin\frac{180°}{4}.cos\frac{180°}{2} + cos\frac{180°}{2}.sin\frac{180°}{3}$

$= tan60°.sin30° + sin45°.cos90° + cos90°.sin60°$

$= \sqrt{3} × \dfrac{1}{2} + \dfrac{1}{\sqrt{2}}×0 + 0 × \dfrac{\sqrt{3}}{2}$

$= \dfrac{\sqrt{3}}{2} + 0 + 0$

$= \dfrac{\sqrt{3}}{2}$

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