Question

if sin A= 8/17 and sinB = 5/13 find the value of sin A cosB+ sinB cosA ​

Answer 1

Step-by-step explanation:

Given :-

Sin A= 8/17

SinB = 5/13

To find:-

Find the value of Sin A CosB+ SinB CosA ?

Solution:-

Given that

Sin A= 8/17 -----------(1)

On squaring both sides then

=> Sin^2 A = (8/17)^2

=> Sin^2 A = 64/289

On subtracting above from 1

=> 1-Sin^2 A = 1-(64/289)

=> 1-Sin^2 A = (289-64)/289

=> 1-Sin^2 A = 225/289

We know that

Sin^2 A + Cos^2 A = 1

=> Cos^2 A = 225/289

=> Cos A =√(225/289)

=> Cos A = 15/17------------------(2)

SinB = 5/13----------------(3)

On squaring both sides then

=> Sin^2 B = (5/13)^2

=> Sin^2 B = 25/169

On subtracting above from 1

=> 1-Sin^2 B= 1-(25/169)

=> 1-Sin^2 B = (169-25)/169

=> 1-Sin^2 B= 144/169

We know that

Sin^2 A + Cos^2 A = 1

=> Cos^2 B = 144/169

=> Cos B =√(144/169)

=> Cos B = 12/13------------------(4)

Now, The value of Sin A CosB+ SinB CosA

From (1),(2),(3)&(4)

=> (8/17)×(12/13)+(5/13)×(15/17)

=> [(8×12)/(17×13)]+[(5×15)/(13×17)]

=> (96/221)+(75/221)

=> (96+75)/221

=> 171/221

Answer:-

The value of Sin A CosB+ SinB CosA for the given problem is 171/221

Used formulae:-

• Sin^2 A + Cos^2 A = 1