Home
Class 11
MATHS
If alpha, beta are different values of t...

If `alpha, beta` are different values of `theta` satisfying the equation `5 cos theta-12 sin theta=11`. If the value of `sin (alpha + beta) =-(5k)/(169)` , then find the value of k.

Text Solution

Verified by Experts

given that, `5cos theta - 12sintheta= 11`
`(5/13)sin theta - (12/13)sin theta = 11/13`
`sin (phi- theta) = 11/13`
let `sin x = sin a`
we can say that `x=a or pi - a`
`phi- theta = alpha- phi or pi-(alpha- phi) `
`pi - (alpha- theta) = (beta- phi)`
`pi- alpha+ phi= beta - phi`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

If alpha, beta are different values of theta satisfying the equation 5 cos theta + 12 sin theta = 11 then the value of sin (alpha + beta)=

If alpha , beta are two different values of theta lying between 0 and 2pi which satisfy the equation 6 cos theta + 8 sin theta=9, find the value of sin ( alpha + beta).

If alpha, beta (alpha ne beta) satisfy the equation a cos theta + b sin theta=c then the value of tan ""(alpha + beta)/(2) is-

If alpha and beta are two different values of theta lying between 0 and 2pi which satisfy the equations 6costheta+8sin theta=9 , find the value of sin2(alpha+beta) .

If alpha and beta are roots of the equation a cos theta + b sin theta = c , then find the value of tan (alpha + beta).

If alpha and beta are roots of the equatioin a cos theta + b sin theta = c , then find the value of tan (alpha + beta).

If alpha and beta are roots of the equatioin a cos theta + b sin theta = c , then find the value of tan (alpha + beta).

If alpha , beta alpha ne beta satisfies the question a costheta + b sin theta = c , then the value of tan ( (alpha + beta)/(2) ) is :

If alpha, beta are solutin of 6 cos theta + 8 sin theta=9, then sin (alpha + beta)=

If alpha and beta are 2 distinct roots of equation a cos theta + b sin theta = C then cos( alpha + beta ) =