Q. 42 C

# Find the value ofsin A. cos B + cos A. sin B. if and tan B = √3.

Given:

Let,

Side opposite to angle A =BC = 1k

Side adjacent to angle A =AB = k√3

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 + (BC)2 = (AC)2

(√3k)2 + (1k)2 = (AC)2

(AC)2 = 1 k2 +3 k2

(AC)2 = 4 k2

AC =2 k2

AC =±2k

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

Now, we will find the sin A and cos A

Side opposite to angle A = BC = k

and Hypotenuse = AC = 2k

So,

Now, we know that,

Side adjacent to angle A = AB =k√3

Hypotenuse = AC =2k

So,

Now,

Given: tan B = √3

Let,

Side opposite to angle B =AC = √3k

Side adjacent to angle B =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 B = AC = k√3

and Hypotenuse = BC = 2k

So,

Now, we know that,

Side adjacent to angle B = AB =1k

Hypotenuse = BC =2k

So,

Now, sin A. cos B + cos A. sin B

Putting the values of sin A, sin B cos A and Cos B, we get

=1

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