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If 5 cos^(2) theta + 1 = 3 sin^(2) theta...

If `5 cos^(2) theta + 1 = 3 sin^(2) theta, 0^(@) lt theta lt 90^(@)`, then what is the value of `( tan theta + sec theta)/( cot theta + cosec theta)` ?

A

` ( 3 + 2 sqrt3)/(3)`

B

`( 2 + 3 sqrt3)/( 3)`

C

`( 2 + 3 sqrt3)/( 2)`

D

`( 3 + 2 sqrt3)/( 2)`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If cot theta + tan theta = 2 sec theta , 0^(@) lt theta lt 90^(@) , then the value of ( tan 2 theta - sec theta)/( cot 2theta + cosec theta) is:

    A
    `( 2 sqrt(3) - 1)/( 11)`
    B
    `( 3 - sqrt(2) )/( 11)`
    C
    `( 2 sqrt(3) -2)/( 11)`
    D
    `( 3- sqrt2)/( 5)`

  • If 12 cos^(2) theta -2 sin^(2)theta +3 cos theta =3, 0^(@) lt theta lt 90^(@) , then what is the value of ("cosec" theta +sec theta)/(tan theta +cot theta) ?

    A
    `(2+sqrt(3))/(4)`
    B
    `(4+sqrt(3))/(4)`
    C
    `(1+2sqrt(2))/(2)`
    D
    `(1+sqrt(3))/(2)`

  • If 11 sin^(2) theta - cos^(2) theta + 4 sin theta - 4 0, 0^(@) lt theta lt 90^(@) , then what is the value of ( cos 2 theta + cot 2 theta)/( sec 2 theta - tan 2 theta) ?

    A
    ` ( 12 + 5 sqrt3)/( 3)`
    B
    `( 10 + 5 sqrt3)/( 3)`
    C
    ` ( 12 + 7 sqrt3)/( 6)`
    D
    `( 10 + 7 sqrt3)/( 6)`

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