If\(\cot \theta = \frac{1}{{\sqrt 3 }}\), 0° <θ° < 90°, then the v

1.	If\(\cot \theta = \frac{1}{{\sqrt 3 }}\), 0° <θ° < 90°, then the value of\(\frac{{2 - {{\sin }^2}\theta }}{{1 - {{\cos }^2}\theta }} + (cose{c^2}\theta - {\sec} \theta )\) is:1. 12. 53. 04. 2
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

If\(\cot \theta = \frac{1}{{\sqrt 3 }}\), 0° <θ° < 90°, then the value of\(\frac{{2 - {{\sin }^2}\theta }}{{1 - {{\cos }^2}\theta }} + (cose{c^2}\theta - {\sec} \theta )\) is:1. 12. 53. 04. 2

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