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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 sin theta + cos theta = a, and sin theta = cos theta = b , then A) a^2 + b^2 = 1 B) a^2 - b^2 = 1 C) a^2 + b^2 = 2 D) a^2 - b^2 = 2

    A
    `a^2 + b^2 = 1 `
    B
    `a^2 - b^2 = 1`
    C
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    D
    `a^2 - b^2 = 2`

  • the value of 1/8 (3-4 cos 2 theta + cos 4 theta ) is

    A
    `cos 4 theta `
    B
    ` sin 4 theta `
    C
    ` sin^4 theta `
    D
    `cos^4 theta`

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