Sum of Trigonometric Ratios in Terms of Their Product
tanπ5 + 2tan2...
Question
tanπ5+2tan2π5+4cot4π5=
A
cotπ5
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B
cot2π5
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C
cot3π5
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D
cot4π5
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Solution
The correct option is Acotπ5 tanπ5+2tan2π5+4cot4π5 Add and subtract cotπ5 =cotπ5−cotπ5+tanπ5+2tan2π5+4cot4π5 Apply this formula cotx−tanx=2×cot2x =cotπ5−4cot4π5+4cot4π5 =cotπ5