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

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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