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If (sin (theta+ alpha))/(cos (theta- alp...

If `(sin (theta+ alpha))/(cos (theta- alpha))=(1-M)/(1+M)` then `Tan ((pi)/(4)- theta). Tan ((pi)/(4)- alpha)=`

A

`(1)/(M)`

B

M

C

`-(1)/(M)`

D

2M

Text Solution

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The correct Answer is:
B
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Suppose that alpha-beta is not an odd multiple of (pi)/2, m in R-{0,-1} an (sin (alpha+beta))/(cos(alpha-beta))=(1-m)/(1+m) . Then show that tan((pi)/4-alpha)=mtan((pi)/4+beta)

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Knowledge Check

  • Tan ((pi)/(4)+theta).Tan((3pi)/(4)+theta)=

    A
    0
    B
    -1
    C
    1
    D
    2

  • If sin ( theta + alpha ) = cos ( theta + alpha ) , then tan theta =

    A
    `(1+ tan alpha)/(1- tan alpha ) `
    B
    `(1- tan alpha )/(1+ tan alpha ) `
    C
    `(tan alpha )/(1 + tan alpha )`
    D
    `(tan alpha )/(1- tan alpha )`

  • Assertion (A) : Suppose that alpha- beta is not an odd multiple of (pi)/(2) , m in R-{0,1) and (sin (alpha+beta))/(cos (alpha-beta))=(1-m)/(1+m) then Tan ((pi)/(4)-alpha)=m cot ((pi)/(4)- beta) Reason (R) : for all C,D, & R cos c+cos D= 2 cos ((C+D)/(2)) cos((C-D)/(2)) cos-cosD=-2sin ((C+d)/(2))sin ((C-D)/(2))

    A
    A is true R, is true ` R rArr A`
    B
    A is true R is true but `R cancel rArr A`
    C
    A is true, R is false
    D
    A is false, R is true

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