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प्रश्न
Write the value of tan 10° tan 15° tan 75° tan 80°?
उत्तर
We have to find: `tan10° tan 15° tan 75° tan 80°`
= `tan10° tan 15° tan 75° tan 80°`
=` tan (90°-80°) tan (90°-75°) tan 75° tan 80°`
=` cot 80° cot 75° tan 75° tan 80°`
= `(cot 75° tan 75°) (cot 80° tan 80°)`
[tan (90°-θ)=cotθ]
= `1xx1` `[cotθ. tan θ=1]`
=1
Hence the value of `tan10° tan 15° tan 75° tan 80°` is 1
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