Q. 175.0( 5 Votes )

# If sin θ = √3 cos θ, then find the values of cos θ and sin θ.

Answer :

Given : sin θ =√3cos θ

⇒ tan θ =√3

We know that,

Or

and tan θ = √3

Let,

The side opposite to angle θ =AC = k√3

The side adjacent to angle θ =AB = 1k

where k is any positive integer

Firstly we have to find the value of BC.

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

⇒ (AB)^{2} + (AC)^{2} = (BC)^{2}

⇒ (1k)^{2} + (k√3)^{2} = (BC)^{2}

⇒ (BC)^{2} = 1 k^{2} +3 k^{2}

⇒ (BC)^{2} = 4 k^{2}

⇒ BC =√2 k^{2}

⇒ BC =±2k

But side BC can’t be negative. So, BC = 2k

Now, we will find the sin θ and cos θ

Side opposite to angle θ = AC = k√3

and Hypotenuse = BC = 2k

So,

Now, we know that,

The side adjacent to angle θ = AB =1k

Hypotenuse = BC =2k

So,

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