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For all values of angle A and B (i)sin(A...

For all values of angle A and B `(i)sin(A-B)=sinAcosB-cosAsinB (ii)sin(A+B)=sinAcosB+cosAsinB`

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For all values of angle A and B(i)cos(A-B)=cos A cos B+sin A sin B(ii)cos(A+B)=cos A cos B-sin A sin B

If A=60^(@) and B=30^(@) , verify that : (i)sin(A-B)=sinAcosB-cosAsinB (ii) cos(A-B)=cosAcosB+sinAsinB (iii) tan(A-B)=(tanA-tanB)/(1+tanAtanB)

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))`

  • For any angles A and B, sin(A+B). sin(A-B)=......

    A
    `sin(A^2-B^2)`
    B
    `sin^2A-sin^2B`
    C
    `cos^2A-cos^2B`
    D
    none of these

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