Question

find cos (π/2+ theta)+cos(3π/2+ theta)+cos(5π/2+theta)+cos(7π/2+theta) upto 2021 terms​

Answer 1

Answer:

cos (π/2 + θ) = -sin θ

cos (3π/2 + θ) = sin θ

cos (5π/2 + θ) = -sin θ ..

.....

The terms are all identical, apart from alternating sign.

There is an odd number of terms; and each adjacent pair sums to zero.

So the sum of 2021 terms = the first (or last) term = -sin θ .