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. √2, √2
• C. 1/√2, 1/√2
• D. 1/√3, 1/√3

Answer 1

The correct option is A

1,1

In right angle triangle ABC,

Let $\angle A$ = ${45}^{\circ }$, $\angle B$ = ${90}^{\circ }$

Then $\angle C$ = ${180}^{\circ }-{90}^{\circ }-{45}^{\circ }$ = ${45}^{\circ }$

Let AB = BC = a

Apply Pythagoras theorem in $△$ABC.

$AC=\sqrt{a^2+a^2}=a\sqrt{2}$

Using Trigonometric ratio,

$cotA=cot{45}^{\circ }=\frac{AB}{BC}$ $=$ $\frac{a\sqrt{2}}{a\sqrt{2}}$ $=1$

$tanC=tan{45}^{\circ }=\frac{AB}{BC}$ $=$ $\frac{a\sqrt{2}}{a\sqrt{2}}$ $=1$