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Question : 21 of 160
Marks:
+1,
-0
Solution:
Let
tan‌A+2‌cot‌2‌A =+| 2‌cos‌2‌A |
| sin‌2‌A |
=+| 2(1−2sin2A) |
| 2‌sin‌A‌cos‌A |
=| sin2A+1−2sin2A |
| sin‌A‌cos‌A |
=| 1−sin2A |
| sin‌A‌cos‌A |
==cot‌A ∴
tan‌α+2‌tan‌2‌α+4‌tan‌4‌α+8‌cot‌8‌α =tan‌α+2‌tan‌2‌α+4(tan‌4‌α+2‌cot‌2(4α)) =tan‌α+2‌tan‌2‌α+4‌cot‌4‌α =tan‌α+2(tan‌2‌α+2‌cot‌2(2α)) =tan‌α+2‌cot‌2‌α=cot‌α
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