Q. 373.7( 3 Votes )

If 4cot θ = 3, show that .

Answer :

Given: cot θ

We know that,



Side adjacent to angle θ =AB = 3k

The side opposite to angle θ =BC = 4k

where k is any positive integer

Firstly we have to find the value of AC.

So, we can find the value of AC with the help of Pythagoras theorem

(AB)2 + (BC)2 = (AC)2

(3k)2 + (4k)2 = (AC)2

(AC)2 = 9k2 +16k2

(AC)2 = 25k2

AC =25k2

AC =±5k

But side AC can’t be negative. So, AC = 5k

Now, we will find the sin θ

Side opposite to angle θ = BC = 4k

and Hypotenuse = AC = 5k


Now, we know that,

Side adjacent to angle θ = AB =3k

Hypotenuse = AC =5k


Now, LHS

= 7 = RHS

Hence Proved

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