Math, asked by Diyamurmu123, 11 months ago

if sinA=4/5 sinB = 5/13 than sin (A+B)=?​

Answers

Answered by rishu6845
7

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

Answered by StyloBabiie
0

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

=56/33

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