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If " "cos alpha+cosbeta=1/3 " and " sina...

`If " "cos alpha+cosbeta=1/3 " and " sinalpha+sin beta=1/4, "show that" " tan"(alpha+beta)/2=3/4`

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If cosalpha+cosbeta=1/3 and sinalpha+sinbeta=1/4 ,show that tan ((alpha+beta)/2)=3/4

If cosalpha+cosbeta=1/3 and sinalpha+sinbeta=1/4 prove that cos(alpha-beta)/2=+-5/24

Knowledge Check

  • If sin 2 alpha + sin 2 beta = 3 "and" cos 2 alpha + cos 2 beta = 4,"then"- tan2 (alpha + beta)=

    A
    `25/7`
    B
    `25/12`
    C
    `25/13`
    D
    `24/7`

  • If x cos alpha + y sin alpha = x cos beta + y sin beta "then" "tan" (alpha + beta)/2=

    A
    `y/x`
    B
    `x/y`
    C
    `(x+y)/y`
    D
    `(x-y)/y`

  • If sin alpha + sin beta = p "and" cos alpha + cos beta = q "then the value of " "tan" (alpha-beta)/2 will be-

    A
    `sqrt((4-p^(2)-q^(2))/(p^(2) + q^(2)))`
    B
    `sqrt((p^(2) + q^(2) - 4)/(p^(2) + q^(2)))`
    C
    `-sqrt((4-p^(2)-q^(2))/(p^(2)+q^(2)))`
    D
    `-sqrt((P^(2) +q^(2)-4)/(p^(2) + q^(2)))`

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    If cos alpha+ cos beta= a sin alpha+ sin beta=b , then show that "tan" (alpha)/(2)+"tan" (beta)/(2)= (4b)/(a^(2)+b^(2)+2a)

    If cosalpha+cosbeta=2/3 and sinalpha+sinbeta=2/5 then find the vvalue of tan((alpha+beta)/2)

    If cos alpha+ cos beta= a and sin alpha+ sin beta =b , then show that sin 2 alpha+ sin 2 beta =2 ab(1- (2)/(a^(2)+ b^(2))) .

    If x cos alpha + y sin alpha=x cos beta+y sin beta,"show that",y=x "tan"(alpha+beta)/2

    If " "2 cos (alpha + beta) cos (alpha-beta)=1, "show that," tan^(2) alpha = (1-tan^(2) beta)/(1+3 tan^(2) beta)

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