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

`30^@`

`60^@`

`120^@`

`150^@`

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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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(1-cos2theta)/(sin2theta)=

`sintheta`

`cos theta`

`tan theta`

none of these

If (cos theta + i sin theta)(cos 2 theta +i sin 2 theta ) …(cos n theta + i sin n theta)=1 then the value of theta is (m are integers)-

`(m pi)/(n (n+1))`

`4m pi`

`(2m pi)/(n (n-1))`

`(4m pi)/(n (n+1))`

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

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(1-cos2theta)/(sin2theta)=

If (cos theta + i sin theta)(cos 2 theta +i sin 2 theta ) …(cos n theta + i sin n theta)=1 then the value of theta is (m are integers)-

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