InterviewSolution
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InterviewSolution
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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]` |
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Answer» Correct Answer - 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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