Q. 24 B3.6( 9 Votes )

# If find the value of cos θ – sin θ.

Answer :

Given: sin θ =√3cos θ

tan θ = 3

We know that,

Or

Given: tan θ = √3

Let,

Side opposite to angle θ =AC = √3k

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 + (√3k)2 = (BC)2

(BC)2 = 1 k2 +3 k2

(BC)2 = 4 k2

BC =2 k2

BC =±2k

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

Now, we will find the sin B and cos B

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,

Now, we have to find the value of cos θ – sin θ

Putting the values of sin θ and cos θ, we get

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