if sinA=4/5 sinB = 5/13 than sin (A+B)=?
Answers
Answer:
Sin ( A + B ) = 53 / 65
Step-by-step explanation:
Given---> SinA = 4/5 , SinB = 5/13
To find ---> Sin(A + B )
Solution---> We know that,
Sin²θ + Cos²θ = 1
=> Cos²θ = 1 - Sin²θ
=> Cosθ = √( 1 - Sin²θ )
Now, CosA = √( 1 - Sin²A)
Putting SinA = 4 / 5 in it , we get
= √{ 1 - ( 4/5 )² }
= √{ 1 - ( 16 / 25 ) }
= √{ (25 - 16) / 25 }
= √(9/25)
= 3 / 5
Now, CosB = √( 1 - Sin²B )
Putting SinB = 5 / 13 in it we get
= √{ 1 - ( 5 / 13 )² }
= √( 1 - 25 / 169 )
= √{( 169 - 25 ) / 169 }
= √( 144 / 169 )
= 12 / 13
Now, we know that
Sin(A + B ) = SinA CosB + CosA SinB
Putting Value of SinA , CosA , SinB , and CosB , we get
= ( 4 / 5 ) ( 12 / 13 ) + ( 3 / 5 ) ( 5 / 13 )
= 48 / 65 + 15 / 65
= (48 + 15 ) / 65
= 53 / 65
Additional formulee--->
1) Sin( A - B ) = SinA CosB - CosA SinB
2) Cos(A + B ) = CosA CosB - SinA SinB
3) Cos ( A - B ) = CosA CosB + SinA SinB
Answer:
Step-by-step explanation:
sinA=4/5 , cotA= 3/4
sinB=5/13 , cotB=12/5
cot(A-B)=( cotA.cotB + 1)/(cotB - cotA)
=( 3/4×12/5 + 1)/(12/5 - 3/4)
=(9/5 + 1)/(48-15/20)
=(9+5)5/(33/20)
=14×4/33