Question

Sin(a+b)=24/25, tana=3/4 then what is the value of cosb

Answer 1

tana = 3/4
so, sina = 3/5 and cosa = 4/5

sin(a + b) = 24/25
a + b = sin-¹(24/25)
b = sin-¹(24/25) - a
take both sides, cos
cosb = cos{ sin-¹(24/25) - a }
= cos.sin-¹(24/25).cosa + sin.sin-¹(24/25).sina
= 7/25 × 4/5 + 24/25 × 3/5
= 28/125 + 72/125
= 100/125
= 4/5

hence, cosb = 4/5

Answer 2

Hi Friend,

Here is your answer,

SO, tan(a) = 3/4 

sin(a)= 3/5 and cos(a) = 4/5 

sin(a + b) = 24/25 

a + b = sin-¹(24/25) 

b => sin-¹(24/25) - a 

Now,we should take cos on both side,

=>cos (b) = cos{ sin-¹(24/25) - a }

=> cos.sin-¹(24/25).cosa + sin.sin-¹(24/25).sina

=> 7/25 × 4/5 + 24/25 × 3/5 

=> 28/125 + 72/125 

=> 100/125 

=> 4/5 

So, the cos (b) => 4/5 


Hope it helps you!