Q. 133.7( 3 Votes )

If sin , then find the value of cos θ and tan θ.

Answer :

Given: Sin θ



We know that,



Or



Let,


Side opposite to angle θ = 12k


and Hypotenuse = 13k


where, k is any positive integer


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


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


(12k)2 + (BCk)2 = (13)2


144 k2 + (BC)2 = 169 k2


(BC)2 = 169 k2 –144 k2


(BC)2 = 25 k2


BC =25 k2


BC =±5k


But side BC can’t be negative. So, BC = 5k


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


We know that,



Side adjacent to angle θ = BC =5k


Hypotenuse = AC =13k


So,


Now, tan θ


We know that,




side opposite to angle θ = AB =12k


Side adjacent to angle θ = BC =5k


So,


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