Question

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

Answer 1

Answer:

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))

]=4

2

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)