Q. 42 A

Find the value ofcos A sin B + sin A. cos B, if sin A= 4/5 and cos B = 12/13.

Given:

To find: cos A sin B + sin A cos B

As, we have the value of sin A and cos B but we don’t have the value of cos A and sin B

So, First we find the value of cos A and sin B

We know that,

Or

Let,

Side opposite to angle A = 4k

and Hypotenuse = 5k

where, k is any positive integer

So, by Pythagoras theorem, we can find the third side of a triangle

(P)2 + (B)2 = (H)2

(4k)2 + (B)2 = (5)2

16 k2 + (B)2 = 25 k2

(B)2 = 25 k2 –16 k2

(B)2 = 9 k2

B =9 k2

B =±3k [taking positive square root since, side cannot be negative]

So, Base = 3k

Now, we have to find the value of cos A

We know that,

Side adjacent to angle A =3k

Hypotenuse =5k

So,

Now, we have to find the sin B

We know that,

Let,

Side adjacent to angle B =12k

Hypotenuse =13k

where, k is any positive integer

So, by Pythagoras theorem, we can find the third side of a triangle

(B)2 + (P)2 = (H)2

(12k)2 + (P)2 = (13)2

144 k2 + (P)2 = 169 k2

(P)2 = 169 k2 –144 k2

(P)2 = 25 k2

P =25 k2

P =±5k [taking positive square root since, side cannot be negative]

So, Perpendicular = 5k

Now, we have to find the value of sin B

We know that,

Now, cos A sin B + sin A cos B

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

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