Q. 43 C5.0( 3 Votes )

# If , prove that :

Given:

We know that,

Let,

BC = 4k and AC = 5k

where, k is any positive integer.

In right angled ∆ABC, we have

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

(AB)2 + (4k)2 = (5k )2

(AB)2 + 16k2 = 25k2

(AB)2 = 25k2 – 16k2

(AB)2 = 9k2

AB = 9k2

AB =±3k [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

Now, RHS =

LHS = RHS

Hence Proved

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