Q. 305.0( 1 Vote )

# If , show that =3.

Given:  We know that,  Let,

BC = 5k and AC = 13k

where, k is any positive integer.

In right angled ∆ABC, we have

(AB)2 + (BC)2 = (AC)2 [by using Pythagoras theorem]

(AB)2 + (5k)2 = (13k )2

(AB)2 + 25k2 = 169k2

(AB)2 = 169k2 – 25k2

(AB)2 = 144k2

AB = 144k2

AB =±12k [taking positive square root since, side cannot be negative]

Now, we have to find the value of other trigonometric ratios.

We, know that    Now, LHS =    =3 =RHS

Hence Proved

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