# $ cosec {69^0} + \cot {69^0}$ When expressed in terms of angles between ${{\text{0}}^0}$ and ${45^0}$ becomes.

$\begin{gathered}

A.{\text{ }}\sec {21^ \circ } + \tan {21^ \circ } \\

B.{\text{ }}\sin {21^ \circ } + \cot {21^ \circ } \\

C.{\text{ }}\sin {21^ \circ } + \cos {21^ \circ } \\

D.{\text{ }}\sec {21^ \circ } + \cot {21^ \circ } \\

\end{gathered} $

Answer

Verified

364.8k+ views

Hint:-Here, we go through the conversion of trigonometric angles.

For this type of question, we have to proceed according to options given, and just we have to change trigonometric functions to get a required option.

We can write ${\text{6}}{{\text{9}}^0}{\text{ = 9}}{{\text{0}}^0} - {21^0}$

And we know that all trigonometric functions are positive in the first quadrant.

Now, we can write question as,

$\cos ec\left( {{{90}^0} - {{21}^0}} \right) + \cot \left( {{{90}^0} - {{21}^0}} \right)$

= $\sec {21^0} + \tan {21^0}$

Here, we know that in first quadrant $\cos ec\left( {{{90}^0} - \theta } \right) = \cot \theta $ and $\cot \left( {{{90}^0} - \theta } \right) = \tan \theta $

Hence option $A$ is the correct answer.

Note:-Whenever we face such a type of question we have to proceed according to the option and remember how to change trigonometric functions.

For this type of question, we have to proceed according to options given, and just we have to change trigonometric functions to get a required option.

We can write ${\text{6}}{{\text{9}}^0}{\text{ = 9}}{{\text{0}}^0} - {21^0}$

And we know that all trigonometric functions are positive in the first quadrant.

Now, we can write question as,

$\cos ec\left( {{{90}^0} - {{21}^0}} \right) + \cot \left( {{{90}^0} - {{21}^0}} \right)$

= $\sec {21^0} + \tan {21^0}$

Here, we know that in first quadrant $\cos ec\left( {{{90}^0} - \theta } \right) = \cot \theta $ and $\cot \left( {{{90}^0} - \theta } \right) = \tan \theta $

Hence option $A$ is the correct answer.

Note:-Whenever we face such a type of question we have to proceed according to the option and remember how to change trigonometric functions.

Last updated date: 24th Sep 2023

â€¢

Total views: 364.8k

â€¢

Views today: 9.64k