Question

If , prove that .

Answer 1

Given:

…… (1)

To prove:

Now we know is defined as follows

…… (2)

Now by comparing equation (1) and (2)

We get,

= 3

= 4

Therefore triangle representing angle is as shown below

Side AC is unknown and can be found using Pythagoras theorem

Therefore,

Now by substituting the value of known sides from figure

We get,

Now by taking square root on both sides

We get,

Therefore Hypotenuse side AC = 5 …… (3)

Now we know, is defined as follows

Therefore from figure (a) and equation (3)

We get,

…… (4)

Now we know

Therefore by substituting the value of from equation (4)

We get,

Therefore,

…… (5)

Now we know, is defined as follows

Therefore from figure (a) and equation (3)

We get,

…… (6)

Now we know

Therefore by substituting the value of from equation (6)

We get,

Therefore,

…… (7)

Now, in expression, by substituting the value of andfrom equation (6) and (7) respectively, we get,

L.C.M of 3 and 4 is 12

Now by taking L.C.M in above expression

We get,

Now 12 gets cancelled and we get,

Now

Therefore,

Now 5 gets cancelled and we get,

Therefore, it is proved that