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Given that 3sinx+4cosx=5 where xin(0,pi/...

Given that `3sinx+4cosx=5` where x`in(0,pi/2)` Find the value of `2sinx+cosx+4tanx`

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Given, `3sinx + 4cosx = 5` `rArr (3/5)sinx + (4/5)cosx = 1` From general triangle `cos53^circ = 3/5` and `sin53^circ = 4/5` `cos53^circsinx + sin53^circcosx = 1` Using formula, `sinAcosB + cosAsinB = sin(A+B)` We have, `sin(x+53^circ) = 1` `sin(x+53^circ) = sin90^circ (∵ x in(0,pi/2))` ...
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Knowledge Check

  • If 3sinx+4cosx=2 , then find the value of 3cosx-4sinx .

    A
    `sqrt(21)`
    B
    5
    C
    0
    D
    `sqrt(29)`

  • If sinx +cosx=(sqrt7)/(2) , where x in [0, (pi)/(4)], then the value of tan.(x)/(2) is equal to

    A
    `(3-sqrt7)/(3)`
    B
    `(sqrt7-2)/(3)`
    C
    `(4-sqrt7)/(4)`
    D
    `(5-sqrt3)/(2)`

  • If 3sinx+4cosx=5 then the value of tan(x//2) is

    A
    `(1pmsqrt(2))/(4)`
    B
    `(-1pmsqrt(2))/(4)`
    C
    `(-1pmsqrt(2))/(3)`
    D
    `1//3`

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    If 0 lt x lt 5/4 and cosx+sinx=5/4 then the value of 16(cosx-sinx)^2 is

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