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प्रश्न
(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to
पर्याय
0
1
−1
None of these
उत्तर
None of these
`(cosec ecθ-sinθ)(secθ-cos θ)(tan θ+cot θ)` Simplifying the given expression, we have
`(cosec θ-sinθ)(secθ-cosθ)(tanθ+cot θ)`
`=(1/sinθ-sinθ)(1/cos^2 θ-cosθ)(sin θ/cos θ+cos θ/sinθ)`
`=1-sin^2θ/sinθ xx(1-cos^2θ)/cos θ xx (sin^2θ+cos^2θ)/(sin θ cos θ)`
=` cos^2θ/sin θ xx sin^2θ/cosθxx1/(sinθ cosθ)`
=`(cos^2θ sin^2θ)/(sin^2θ cos^2θ)`
= `1`
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