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Using the fact: sin(A+B)=sinAcosB+cosAsi...

Using the fact: `sin(A+B)=sinAcosB+cosAsinB` and the technique of differentiation, obtain the sum formula for cosines.

Text Solution

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Given that,
`y=sin(A+B)=sinAcosB+cosAsinB`
Let, `A` be variable and `B` be constant
Differentiating w.r.t. `A`
We know that,
`frac{d(sinx)}{dx}=cosx, frac{d(cosx)}{dx}=-sinx`
`(dy)/(dx)=cos(A+B)=cosAcosB-sinAsinB`

Answer is: ...
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Knowledge Check

  • If sin(A-B)=sinAcosB-cosAsinB , then sin15^(@) will be

    A
    `(sqrt(3)+1)/(2sqrt(2))`
    B
    `(sqrt(3))/(2sqrt(2))`
    C
    `(sqrt(3)-1)/(-sqrt(2))`
    D
    `(sqrt(3)-1)/(2sqrt(2))`

  • sin^(2)A+sin^(2)(A-B)+2sinAcosB sin(B-A) is equal to

    A
    `sin^(2)A`
    B
    `sin^(2)B`
    C
    `cos^(2)A`
    D
    `cos^(2)B`

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