3sin43π2-α+sin43π+α-2sin6π2+α+sin65π-α=?
0
1
3
sin4α+sin6α
Explanation for the correct option:
Step-1: Simplify the given data.
Given, 3sin43π2-α+sin43π+α-2sin6π2+α+sin65π-α
3sin43π2-α+sin43π+α-2sin6π2+α+sin65π-α=3cos4α+sin4α-2cos6α+sin6α=3cos2α2+sin2α2-2cos2α3+sin2α3=3cos2α2+sin2α2+2cos2αsin2α-2cos2αsin2α-2cos2α+sin2αcos4α+sin4α-sin2αcos2α=3cos2α+sin2α2-2cos2αsin2α-2cos2α+sin2αcos4α+sin4α-sin2αcos2α
Step-2: Apply, property sin2θ+cos2θ=1.
=31-2cos2αsin2α-21×cos4α+sin4α-sin2αcos2α
Step-3: Apply formula cos2α+sin2α2-2cos2αsin2α
=31-2cos2αsin2α-2cos2α+sin2α2-2cos2αsin2α-sin2αcos2α=31-2cos2αsin2α-21-3cos2αsin2α=3-6cos2αsin2α-2+6cos2αsin2α=1
Therefore, correct answer is option B
The value of tan α+2tan(2α)+4tan(4α)+.....+2n−1tan(2n−1α)+2ncot(2nα) is