Evaluate: (2𝑠𝑖𝑛 2 60 − 𝑡𝑎𝑛 2 30) / 𝑠𝑒𝑐2 45

Q) Evaluate: (2𝑠𝑖𝑛 2 60⁰ − 𝑡𝑎𝑛 2 30⁰) / 𝑠𝑒𝑐2 45⁰

Ans:

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

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

$\frac{2 \sin^2 60 - \tan ^2 30}{\sec ^2 45}$

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

= $\frac{2 (\frac{3}{4}) - (\frac{1}{3})}{(2)}$

= $\frac{(\frac{3}{2}) - (\frac{1}{3})}{(2)}$

= $\frac{(\frac{7}{6})}{(2)}$

= $\frac{7}{12}$

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