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If 0 le theta lepi and 8 1^(sin^2theta)...

If `0 le theta lepi and 8 1^(sin^2theta)+8 1^(cos^2theta)=30` is

A

`30^@`

B

`60^@`

C

`120^@`

D

`150^@`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`cos^2theta=1-sin^2theta`.
Let `81^(sin^2theta)=z`,we get
`z+81/z=30`
`or z^2-30z+81=0`
`or 9z-27)(z-3)=0`
`i.e., 81^sin^2theta=3(4sin^2theta)=3^3or3^1`
`:. sin^2theta=3/4,1/4`
`or sintheta=pmsqrt3/2,pm1/2`
`:. theta=30^@,60^@,120^@,150^@`
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Knowledge Check

  • If 0le theta le pi and 81^(sin^(2) theta ) + 81^(cos^(2) theta ) = 30 then theta is

    A
    `30^(@)`
    B
    `60^(@)`
    C
    `120^(@)`
    D
    `150^(@)`

  • The value of theta in (0, (pi)/(2)) satisfying |(1+sin^(2) theta,cos^(2) theta, 4 sin 4 theta),(sin^(2) theta , 1+cos^(2) theta,4 sin 4 theta),(sin^(2) theta, cos^(2) theta, 1+4 sin 4 theta)|=0 are

    A
    `(7 pi)/(24)`
    B
    `(5 pi)/(24)`
    C
    `(13 pi)/(24)`
    D
    `(pi)/(24)`

  • (1+sin 2theta+cos 2theta)/(1+sin2 theta-cos 2 theta) =

    A
    `(1)/(2)tan theta`
    B
    `(1)/(2)cot theta`
    C
    `tan theta`
    D
    `cot theta`

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