Q. 403.7( 3 Votes )

If , prove that q sin θ = p.

Answer :

Given : q cos θ = √(q2 – p2)



We know that,



Or



Let,


Base =BC = √(q2 – p2)


Hypotenuse =AC = q


Where, k ia any positive integer


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


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


(AB)2 + (√(q2 – p2))2 = (q)2


(AB)2 + (q2 – p2) = q2


(AB)2 = q2 q2 + p2)


(AB)2 = p2


AB =p2


AB =±p


But side AB can’t be negative. So, AB = p


Now, we have to find sin θ


We know that,



The side opposite to angle θ = AB =p


And Hypotenuse = AC =q


So,


Now, LHS = q sin θ



= q = RHS


Hence Proved


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