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प्रश्न
The value of tan 1° tan 2° tan 3° ...... tan 89° is
विकल्प
1
−1
0
None of these
उत्तर
Here we have to find: `tan 1°tan 2° tan 3°........... tan 89°`
`tan1° tan 2° tan 3°............... tan 89°`
`=tan (90°-89°) tan (90°-88°)tan (90°-87°).............. tan 87° tan88° tan 89°`
`= cot 89° cot 88° cot 87°............tan 87° tan 88° tan 89°`
`= (cot 89° tan 89°)(cot 88° tan 88°) (cot 87° tan 87°).....(cot 44° tan 44°) tan 45°`
= `1xx1xx1............1xx1` `["since cot θ tan θ=1"]`
=`1`
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