Question

Match the following:

$\begin{array}{cc}1.\text{sin}({90}^{\circ }-A)& a)\text{cosec}A\\ 2.\text{tan}({90}^{\circ }-A)& b)\text{cot}A\\ 3.\text{sec}({90}^{\circ }-A)& c)\text{cos}A\end{array}$

• A. 1- c; 2 - b; 3 - a
• B. 1 - a; 2 - b; 3 - c
• C. 1 - a; 2 - c; 3 - b
• D. 1 - b; 2 - c;3 - a

Answer 1

The correct option is A

1- c; 2 - b; 3 - a

In the right triangle ABC, right angled at B;

As, sum of all the angles of a triangle $={180}^{\circ }$

We have, $\angle A+\angle C={90}^{\circ }$

$\Rightarrow \angle C={90}^{\circ }-\angle A$

$\cos A=\frac{AB}{AC}=\sin C=\sin ({90}^{\circ }-A)$

$cosecA=\frac{AC}{BC}=\sec C=sec({90}^{\circ }-A)$

$\cot A=\frac{AB}{BC}=\tan C=\tan ({90}^{\circ }-A)$