Q. 195.0( 4 Votes )

If sin θ = cos θ and 0° < θ <90°, then find the values of sin θ and cos θ.

Answer :

Given: sinθ = cosθ


tan θ = 1




Let,


Side opposite to angle θ = AB =1k


The side adjacent to angle θ = BC =1k


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


(1k)2 + (1k)2 = (AC)2


(AC)2 = 1k2 +1k2


(AC)2 = 2k2


AC =2k2


AC =k2


So, AC = k√2


Now, we will find the sin θ



Side opposite to angle θ = AB= 1k


and Hypotenuse = AC = k√2


So,


Now, we know that,



The side adjacent to angle θ = BC =1k


Hypotenuse = AC =k√2


So,


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