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If theta and phi are acute angles satisf...

If `theta` and `phi` are acute angles satisfying `sin theta=1/2, cos phi=1/3` then `theta+phi=`

A

`(pi/(3), (pi)/(6)]`

B

`((pi)/(2), (2pi)/(3))`

C

`((2pi)/(3),(5pi)/(6))`

D

`((5pi)/(6),pi]`

Text Solution

Verified by Experts

The correct Answer is:
B
Since, `sin theta = (1)/(2)`
and cos `phi = (1)/(3) implies thet = (pi)/(6)`
and `0 lt (cos phi - (1)/(3)) lt (1)/(2) " "["as " 0 lt (1)/(3) lt (1)/(2)]`
`implies theta = (pi)/(6) and cos^(-1)(0) gt phi gt cos^(-1) ((1)/(2))`
[the sign changed as cos x is decreasing between `(0, (pi)/(2))`]
`implies theta = (pi)/(6) and (pi)/(3) lt phi lt (pi)/(2) implies (pi)/(2) lt theta + phi lt (2pi)/(3)`
`therefore" " theta in ((pi)/(2), (2pi)/(3)) `
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