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If 1/6 sin theta , cos theta and tan the...

If `1/6 sin theta , cos theta and tan theta ` are in GP, then find the general solution for ` theta `

A

`2npi+-pi/3`

B

`2npi+-pi/6`

C

`npi+-pi/3`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
Since, `1/6sintheta,costheta, tantheta` are in G.P.
`rArr cos^(2)theta=1/6(sintheta.tantheta) rArr 6cos^(3)theta+cos^(2)theta-1=0`
`therefore (2costheta-1)(3 cos^(2)theta+2costheta+1)=0`
`rArr costheta=1/2` (other values of `costheta` are imaginary)
`rArr costheta=cospi/3 rArr theta=2npi+-pi/3, n in I`.
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