# $ 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} $

Last updated date: 26th Mar 2023

•

Total views: 310.2k

•

Views today: 2.90k

Answer

Verified

310.2k+ 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.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE