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If alpha = cos^(-1)(3/5), beta = tan^(-1...

If `alpha = cos^(-1)(3/5), beta = tan^(-1)(1/3)`, where `0 lt alpha, beta lt pi//2`, then `alpha - beta` is equal

A

`tan^(-1)(9/(5sqrt(10)))`

B

`cos^(-1)(9/(5sqrt(10)))`

C

`tan^(-1)(9/13)`

D

`sin^(-1)(9/(5sqrt(10)))`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • If alpha=cos^(-1)((3)/(5)),beta=tan^(-1)((1)/(3)), where 0

    A
    `tan^(-1)((p)/(5sqrt(10)))`
    B
    `cos^(-1)((9)/(5sqrt(10)))`
    C
    `tan^(-1)((9)/(14))`
    D
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  • If cos(alpha+beta)=(3)/(5), sin(alpha-beta)=(5)/(13) and 0 lt alpha, beta lt (pi)/(4) then tan(2alpha) is equal to

    A
    `63//52`
    B
    `63//16`
    C
    `21//16`
    D
    `33//52`

  • If sin ( 120^(@) - alpha ) = sin ( 120^(@) - beta ), 0 lt alpha, beta lt pi , then alpha and beta are given by

    A
    `alpha = beta`
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    `alpha = beta` or `alpha + beta = ( pi )/( 3)`
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    D
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