Question

The value of \[\cos ec{{30}^{\circ }}+\cot {{45}^{\circ }}\] is:

A. 2
B. 1
C. 3
D. -1

Answer 1

Hint:
From the trigonometric table get the value of \[\cos ec{{30}^{\circ }}\] and \[\cot {{45}^{\circ }}\]. Thus substitute the values in the expression and find the sum.

Complete step-by-step answer:
We can use the trigonometric table to solve the above expression. The trigonometric table helps us to find the values of trigonometric ratios- sine, cosine, tangent, cosecant, secant, cotangent, i.e. they can be written as sin, cos, tan, cosec, sec, cot.

Angles (degree)	\[{{0}^{\circ }}\]	\[{{30}^{\circ }}\]	\[{{45}^{\circ }}\]	\[{{60}^{\circ }}\]	\[{{90}^{\circ }}\]
Angles (radian)	0	\[{}^{\pi }/{}_{6}\]	\[{}^{\pi }/{}_{4}\]	\[{}^{\pi }/{}_{3}\]	\[{}^{\pi }/{}_{2}\]
Sin	0	\[{}^{1}/{}_{2}\]	\[{}^{1}/{}_{\sqrt{2}}\]	\[{}^{\sqrt{3}}/{}_{2}\]	1
Cos	1	\[{}^{\sqrt{3}}/{}_{2}\]	\[{}^{1}/{}_{\sqrt{2}}\]	\[{}^{1}/{}_{2}\]	0
Tan	0	\[{}^{1}/{}_{\sqrt{3}}\]	1	\[\sqrt{3}\]	N.A.
Cot	N.A.	\[\sqrt{3}\]	1	\[{}^{1}/{}_{\sqrt{3}}\]	0
Cosec	N.A.	2	\[\sqrt{2}\]	\[{}^{2}/{}_{\sqrt{3}}\]	1
Sec	1	\[{}^{2}/{}_{\sqrt{3}}\]	\[\sqrt{2}\]	2	N.A.

We have been given the expression \[\cos ec{{30}^{\circ }}+\cot {{45}^{\circ }}\].
Thus from the trigonometric table we can get the values of \[\cos ec{{30}^{\circ }}\] and \[\cot {{45}^{\circ }}\].
From the trigonometric table,
\[\cos ec{{30}^{\circ }}=2\] and \[\cot {{45}^{\circ }}=1\]
\[\therefore \cos ec{{30}^{\circ }}+\cot {{45}^{\circ }}=2+1=3.\]
Thus we got the value of \[\cos ec{{30}^{\circ }}+\cot {{45}^{\circ }}\] as 3.
Option C is the correct answer.

Note: The value of trigonometric ratios is standard angles and is very important to solve the trigonometric problems. Therefore it is necessary to remember the values of trigonometric ratios and of these standard values.