Question

Which of the following statement is correct?

• A. $cos({90}^{\circ }-A)=sinA$
• B. $tan({90}^{\circ }-A)=cotA$
• C. Both A and B
• D. None of the above

Answer 1

The correct option is C

Both A and B

In ΔABC, right-angled at B, (i.e. ∠B=${90}^{\circ }$ )

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

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

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

So,

$sinA=\frac{BC}{AC}$

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

$\Rightarrow cos({90}^{\circ }-A)=sinA$

Similarly,

$cotA=\frac{AB}{BC}$

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

$\Rightarrow tan({90}^{\circ }-A)=cotA$