# If , prove that

Given: Sin θ

We know that,

Or

Let,

Perpendicular =AB =m

and Hypotenuse =AC =√(m2 + n2)

where, k is any positive integer

So, by Pythagoras theorem, we can find the third side of a triangle

In right angled ABC, we have

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

(m)2 + (BC)2 = (√(m2 + n2))2

m2 + (BC)2 = m2 + n2

(BC)2 = m2 + n2 – m2

(BC)2 = n2

BC =n2

BC =±n

But side BC can’t be negative. So, BC = n

Now, we have to find the value of cos θ and tan θ

We know that,

Side adjacent to angle θ or base = BC =n

Hypotenuse = AC =√(m2 + n2)

So,

Now, LHS = m sin θ +n cosθ

=√(m2 + n2) = RHS

Hence Proved

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