Answer :

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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