Question

In triangle ABC, right angled at B, if $\angle A$ is ${45}^{\circ }$, find the value of cot A and tan C, without using tables.

• 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

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

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

Let AB = BC = a [since $\angle B$ and $\angle C$ = ${45}^{\circ }$, its an isosceles right triangle]

Apply Pythagoras theorem in $△$ABC

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

Using Trigonometric ratio

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

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