Evaluate the following: $$\dfrac{cos\; 45°}{sec \;30°+cosec \;30°}$$

Asked by Pragya Singh | 1 year ago |  91

##### Solution :-

We know that,

cos 45° = $$\dfrac{1}{\sqrt{2}}$$

sec 30° = $$\dfrac{2}{\sqrt{3}}$$

cosec 30° = 2

Substitute the values, we get

Now, multiply both the numerator and denominator by $$\sqrt{2}$$ , we get

Therefore, $$\dfrac{cos\; 45°}{(sec \;30°+cosec \;30°)}= \dfrac{3\sqrt{2}-\sqrt{6}}{8}$$

Answered by Abhisek | 1 year ago

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