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If tan alpha, tan beta are the roots of ...

If `tan alpha, tan beta` are the roots of the equation `x^(2)+px+q=0` then `sin^(2) (alpha+ beta)+ p sin(alpha+ beta) (cos+beta) +q cos^(2)(alpha+ beta)=`

A

0

B

1

C

p

D

q

Text Solution

Verified by Experts

The correct Answer is:
D
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Knowledge Check

  • If tan alpha, tan beta are the roots of the equation x^(2)+px+q=0(p ne 0) then sin^(2)(alpha+beta)+p sin (alpha+beta)cos(alpha+beta)+q cos^(2)(alpha+beta)=

    A
    0
    B
    1
    C
    p
    D
    q

  • If tan alpha , tan beta are the roots of the equation x^(2) + px+q=0(p ne 0) then

    A
    `cos(alpha + beta)=1-q`
    B
    `sin (alpha + beta )=-p`
    C
    `tan(alpha + beta )=p//(q-1)`
    D
    none

  • If tan alpha and tan beta are the roots of the equation x^(2) +px + q = 0 , then the value of sin^(2) (alpha +beta) + p cos (alpha + beta) sin (alpha + beta) + q cos^(2) (alpha + beta) is

    A
    p + q
    B
    p
    C
    q
    D
    `(p)/(p +q)`

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