If \(\cot \theta = \frac{1}{{\sqrt 3 }}\), 0°

1.	If \(\cot \theta = \frac{1}{{\sqrt 3 }}\), 0°
Answer» Correct Answer - Option 1 : 1 Given: \(\cot \theta = \frac{1}{{\sqrt 3 }}\) θ = 60° Calculation: sin 60° =\(\frac{{\sqrt 3 }}{2}\) cos 60° = \(\frac{1}{2}\) cosec 60° =\(\frac{2}{\sqrt3}\) sec 60° = 2 substituting the value in the given expression = \(\frac{2-\frac{3}{4}\ }{1-\frac{1}{4}}+(\frac{4}{3}\ -2)\) ⇒\(\frac{\frac{5}{4}\ }{\frac{3}{4}}-\frac{2}{3}\) = \(\frac{{5\;}}{3} - \frac{2}{3} = 1\) ∴ the value for the \(\frac{{2 - {{\sin }^2}\theta }}{{1 - {{\cos }^2}\theta }} + (cose{c^2}\theta - {\sec} \theta )\) = 1

Answer» Correct Answer - Option 1 : 1

Given:

\(\cot \theta = \frac{1}{{\sqrt 3 }}\)

θ = 60°

Calculation:

sin 60° =\(\frac{{\sqrt 3 }}{2}\)

cos 60° = \(\frac{1}{2}\)

cosec 60° =\(\frac{2}{\sqrt3}\)

sec 60° = 2

substituting the value in the given expression

= \(\frac{2-\frac{3}{4}\ }{1-\frac{1}{4}}+(\frac{4}{3}\ -2)\) ⇒\(\frac{\frac{5}{4}\ }{\frac{3}{4}}-\frac{2}{3}\)

= \(\frac{{5\;}}{3} - \frac{2}{3} = 1\)

∴ the value for the \(\frac{{2 - {{\sin }^2}\theta }}{{1 - {{\cos }^2}\theta }} + (cose{c^2}\theta - {\sec} \theta )\) = 1

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