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Minimum and maximu value of tan theta=……...

Minimum and maximu value of `tan theta`=……….

A

`(- infty, infty)`

B

`(- infty, 0)`

C

(3, 2)

D

(1, -1)

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{:("Column -I","Column - II"),("A) If maximum and minimum values of" ( 7+6 tan theta - tan^(2) theta)/(( 1 + tan^(2) theta) ) "for all real values of" theta ne (2n+1) (pi)/(2) "are" lambda " and u respectively then","p)" lambda+ mu =2),("B) If maximum and minimum values of" 5 cos theta + 3 cos ( theta + (pi)/(3) +3)"for all real values of" theta "are" lambda "and u respectively then" ,"q)" lambda- mu =6),("C) If maximum and minimum values of" 1+ sin((pi)/(4) + theta) + 2cos ((pi)/(4) - theta) "for all real values of" theta "are" lambda and mu "respectively then","s)" lambda- mu = 10),(,"t)" lambda- mu =14):}

If sec theta + tan theta= 5 , find the quadrant in which theta lies and find the value of sin theta .

Knowledge Check

  • The minimum and maximum values of cos theta + 2 sqrt(2) sin theta is

    A
    `3,3`
    B
    `3,-3`
    C
    `[-3,3]`
    D
    `[0,3]`

  • If tan theta = n tan phi then the maximum value of tan^(2)(theta-phi) is equal to

    A
    `((n+1)^(2))/(4n)`
    B
    `((n-1)^(2))/(4n)`
    C
    `((n+1)^(2))/(2n)`
    D
    `((n-1)^(2))/(2n)`

  • The minimum value of a tan^(2)x + b cot^(2)x equals the maximum value of asin^(2) theta+b cos^(2) theta where a gt b gt 0. Then a/b is.

    A
    2
    B
    4
    C
    6
    D
    8

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    Statement I : Minimum value of (3 sn theta -4 cos theta ) ( 3 cos theta + 4 sin theta ) is -(25)/(2) Statement II : Minimum value of 9 tan^(2) x+ 16 cot^(2) x is 24 Which of the above statement is correct ?

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