Question

In triangle ABC, right angled at B, if $\angle A$ is ${45}^{\circ }$, find the value of cot A and tan C.

• A. 1, 1
• B. $\sqrt{2}$, $\sqrt{2}$
• C. $\frac{1}{\sqrt{2}}$, $\frac{1}{\sqrt{2}}$
• D. $\frac{1}{\sqrt{3}}$, $\frac{1}{\sqrt{3}}$

Answer 1

The correct option is A

1, 1

In right angle triangle ABC,

$\angle B$ = ${90}^{\circ }$ and $\angle A$ = ${45}^{\circ }$.

Then $\angle C$ = ${180}^{\circ }-{90}^{\circ }-{45}^{\circ }$ = ${45}^{\circ }$ (using angle sum property)

cot A = cot ${45}^{\circ }$ = 1

tan C = tan ${45}^{\circ }$ = 1