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If sin alpha=A sin(alpha+beta),Ane0, the...

If `sin alpha=A sin(alpha+beta),Ane0`, then
The value of `tan alpha` is

A

`(Asin beta)/(1-Acosbeta)`

B

`(Asin beta)/(1+A cos beta)`

C

`(A cos beta)/(1-A sin beta)`

D

`(A sin beta)/(1+A cos beta)`

Text Solution

Verified by Experts

The correct Answer is:
A
`sin alpha = A sin ( alpha+ beta) = A( sin alpha cos beta + sin beta cot alpha ) `
`rArr sin alpha (1-A cos beta) = A sin beta cos alpha " " `…(i)
`rArr tan alpha = (Asin beta ) /((1-A cos beta))" " `…(ii)
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Knowledge Check

  • If sin alpha=A sin(alpha+beta),Ane0 , then The value of tan beta is

    A
    `(sinalpha(1+A cos beta))/(A cos alpha cos beta)`
    B
    `(sinalpha(1-A cos beta))/(A cos alpha cos beta)`
    C
    `(cos (1-A sinbeta))/(A cos alpha cos beta)`
    D
    `(cos alpha(1+A sin beta))/(A cos alpha cos beta)`

  • If sin alpha=A sin(alpha+beta),Ane0 , then Which of the following is not the value of tan(alpha+beta) ?

    A
    `(sin beta)/(cos beta-A)`
    B
    `(sin alpha cos alpha)/(A cos beta-sin^(2)alpha)`
    C
    `(sin alpha cos alpha)/(A cos beta+sin^(2)alpha)`
    D
    none of these.

  • If 3 sin beta = sin(2alpha +beta) , then tan (alpha+beta)-2 tan alpha is

    A
    independent of `alpha`
    B
    independent of `beta`
    C
    independent of both `alpha and beta`
    D
    independent of none of them

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