Evaluate : (cos 45° + sin 60°) / (sec 30° + cosec 30°)

Q) Evaluate : (cos 45⁰ + sin 60⁰) / (sec 30⁰+ cosec 30⁰).

Ans:

We know that: cos 45⁰ = $\frac{1}{\sqrt 2}$ ; sin 60⁰ = $\frac{\sqrt 3}{2}$ ; sec 30⁰ = $\frac{2}{\sqrt 3}$ ; cosec 30⁰ = 2

By submitting these values in the given expression, we get:

(cos 45⁰ + sin 60⁰) / (sec 30⁰+ cosec 30⁰)

= $\frac{(\frac{1}{\sqrt 2} + \frac{\sqrt 3}{2})}{(\frac{2}{\sqrt 3} + 2)}$

= $\frac{(\frac{2 + \sqrt 6}{2\sqrt 2})}{(\frac{2 + 2 \sqrt 3}{\sqrt 3})}$

= $\frac{(\sqrt 3)(2 + \sqrt 6)}{(2\sqrt 2)(2 + 2 \sqrt 3)}$

= $\frac{(2 \sqrt 3 + \sqrt 18)}{(4\sqrt 2 + 4 \sqrt 6)}$

= $\frac{(2 \sqrt 3 + 3\sqrt 2)}{(4\sqrt 2 + 4 \sqrt 6)}$

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