Question

If 3 cot A = 4, check whether $\frac{1-{\tan }^{2}A}{1+{\tan }^{2}A}={\cos }^{2}A-{\sin }^{2}A$ or not.

Answer 1

Given:

To check whether or not

Dividing by 3 on both sides,

We get,

…… (1)

By definition,

Therefore,

…… (2)

Comparing Equation (1) and (2)

We get,

= 4

= 3

Hence, is as shown in figure below

In, Hypotenuse is unknown

Hence, It can be found by using Pythagoras theorem

Therefore by applying Pythagoras theorem in

We get

Hence, Hypotenuse = 5

To check whether or not

We get the values of

By definition,

Substituting the value from Equation (1)

We get,

….… (3)

Now by definition,

…… (4)

Now by definition,

…… (5)

Now we first take L.H.S of Equation

Substituting value of from equation (3)

We get,

Taking L.C.M on both numerator and denominator

We get,

…… (6)

Now we take R.H.S of Equation

Substituting value of and from equation (4) and (5)

We get,

…… (7)

Comparing Equation (6) and (7)

We get,

Answer: Yes