Question

Match the following:

$$\begin{array}{cc}1.cos({90}^{\circ }-A)& a)secA\\ 2.cot({90}^{\circ }-A)& b)tanA\\ 3.cosec({90}^{\circ }-A)& c)sinA\end{array}$$

• 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

$sinA=\frac{BC}{AC}=cosC=cos({90}^{\circ }-A)$

$secA=\frac{AC}{AB}=cosecC=cosec({90}^{\circ }-A)$

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