The value of 2cot2π6+4tan2π6-3cosecπ6 is
2
4
43
34
Explanation for the correct answer:
tanπ6=13
⇒ cotπ6=1tanπ6=3
1+cot2θ=cosec2θ
⇒ 1+32=cosec2π6
⇒ cosec2π6=4
⇒ cosecπ6=2
The given expression is 2cot2π6+4tan2π6-3cosecπ6
Substituting all the values, we get
2cot2π6+4tan2π6-3cosecπ6=232+4132-32
=6+43-6
⇒ 2cot2π6+4tan2π6-3cosecπ6=43
Hence, the value of the expression 2cot2π6+4tan2π6-3cosecπ6 is 43
Hence, option (C) is the correct answer.