Question

Match the following:

$$\begin{array}{cc}1.sin({90}^{\circ }-A)& a)cosecA\\ 2.tan({90}^{\circ }-A)& b)cotA\\ 3.sec({90}^{\circ }-A)& c)cosA\end{array}$$

• 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, ∠ A + ∠ C = ${90}^{\circ }$

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

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

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

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