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Question : 117 of 150
Marks:
+1,
-0
Solution:
tan‌9∘−tan‌27∘−tan‌63∘+tan‌81∘=tan‌9∘−tan‌27∘−tan(90∘−27∘)+tan(90∘−9∘)=tan‌9∘−tan‌27∘−cot‌27∘+cot‌9∘=‌+‌−‌−‌=‌| sin‌29∘+cos29∘ |
| cos‌9∘⋅sin‌9∘ |
−‌| sin‌227∘+cos227∘ |
| cos‌27∘⋅sin‌27∘ |
=‌−‌(∵2sin‌A⋅cos‌A=sin‌2A)=2(‌| sin‌54∘−sin‌18∘ |
| sin‌18∘⋅sin‌54∘ |
)=2[‌| 2‌cos()⋅sin‌() |
| sin‌18∘⋅sin‌54∘ |
]=4(‌| cos‌36∘⋅sin‌18∘ |
| sin‌18∘⋅sin‌54∘ |
)=4{‌| cos(90∘−54∘) |
| sin‌54∘ |
} =4(‌)=4
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