1.

If `AxxB=1, A+B="cosec"theta*sec theta` then `(A)/(B)` can be _______A. `tan^(2) theta `B. `sec^(2) theta `C. `sin^(2)theta cos^(2) theta `D. `"cosec"^(2) theta sec^(2)theta `.

Answer» Correct Answer - A
`AB=1impliesA=(1)/(B)`
`A+B=(1)/(sin theta)(1)/(costheta)=(1)/(sin theta cos theta )=(sin^(2)theta+cos^(2)theta)/(sin theta cos theta)`
`A+B=(sin theta)/(costheta)+(cos theta )/( sin theta )`
`A+B=tan theta + cot theta`.
Since,`tan theta xx cot theta=1=AB`.
`:. A= tan theta, B=cot theta`.
`(A)/(B)=(tan theta )/( cot theta )=tan theta * tan theta =tan^(2)theta`.
`A= cot theta, B=tan theta,(A)/(B)=cot^(2)theta`


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