Question

One of the Trigonometric ratios is given below. Find The remaining Trigonometric ratios:-
1. CotA = 1​

Answer 1

Answer:

Consider the figure given above.

Here (with respect to angle A) :

Hypotenuse = AC.

Adjacent = AB.

Opposite = BC.

Given:

CotA = 1.

That is,

Adjacent/Opposite = 1.

That is,

AB/BC = 1.

So,

AB = BC.

Let,

AB = BC = k (where k > 0).

By Pythagoras theorem,

(Hypotenuse)² = (Base)² + (Altitude)².

Here,

Hypotenuse = AC.

Base = AB.

Altitude = BC.

That is,

(AC)² = (AB)² + (BC)².

Substituting the values, we get,

(AC)² = k² + k²

(AC)² = 2•k²

AC = √(2•k²)

AC = (√2•k)

To find remaining Trigonometric ratios:

→ SinA = Opposite/Hypotenuse = BC/AC = k/(√2•k) = 1/(√2).

→ CosA = Adjacent/Hypotenuse = AB/AC = k/(√2•k) = 1/(√2).

→ TanA = Opposite/Adjacent = BC/AB = k/k = 1.

→ CosecA = Hypotenuse/Opposite = AC/BC = (√2•k)/k = √2 .

→ SecA = Hypotenuse/Adjacent = AC/AB = (√2•k)/k = √2.