Question

$\sf\sec \bigg( \sum \limits^{2018}_{k = - 1} \csc( \tan( \cot( \sin( \cos( \frac{4k + 5}{20} \pi ) ) ) ) ) \bigg )$​

Answer 1

Answer:

Correct option is

C

12π

D

125π

Given :

sin(π/4)1[sinθsin(θ+π/4)sin(θ+π/4−θ)+sin(θ+π/4)⋅sin(θ+π/2)sin(θ+π/2−(θ+π/4))+…+sin(θ+3π/2)⋅sin(θ+5π/4)sin((θ+3π/2)−(θ+5π/4))]=42

Using Formula for splitting numerator of first term:

sin(θ+π/4−θ)=sin(θ+π/4)cos(θ)−cos(θ+π/4)sin(θ)

⇒2[cotθ−cot(θ+π/4)+cot(θ+π/4)−cot(θ+π/2)+…+cot(θ+5π/4)−cot(θ+3π/2)]=42

⇒tanθ+cotθ=4⇒tanθ=2±3