Q. 324.3( 3 Votes )

If 5 tan α = 4, show that .

Answer :

Given: 5 tan = 4

tan α



We know that,



Or



Let,


The side opposite to angle α =AB = 4k


The side adjacent to angle α =BC = 5k


where k is any positive integer


Firstly we have to find the value of AC.


So, we can find the value of AC with the help of Pythagoras theorem


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


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


(AC)2 = 16k2+25k2


(AC)2 = 41k2


AC =41k2


AC =±k41


But side AC can’t be negative. So, AC = k√41


Now, we will find the sin α and cos α


We know that



Side adjacent to angle α = BC = 5k


and Hypotenuse = AC = k√41


So,


And


Side adjacent to angle α =AB = 4k


And Hypotenuse =AC = k√5


So,


Now, LHS





= RHS


Hence Proved


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