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प्रश्न
tan 5° ✕ tan 30° ✕ 4 tan 85° is equal to
विकल्प
`4/sqrt3`
`4sqrt3`
1
4
उत्तर
We have to find `tan 5°xx tan 30° xx4 tan 85°`
We know that
`tan (90°-θ)=cot-θ`
`tan θ cot -θ=1`
`tan 30°=1/sqrt3`
so
`tan 5° xx tan 30° xx 4 tan 85°`
=` tan (90°-85°)xx tan 30°xx4 tan 85°`
= `cot 85° xx tan 30°xx4 tan 85°`
=` 4 cot 85° xx tan 85° tan 30°`
= `4xx1xx1/sqrt3`
= `4/sqrt3`
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