Question

If for k Ī N, = 2[cos x + cos 3x +......+ cos (2k –1) x], then value of I = is

• A. –p/2
• B. 0
• C. p/2
• D. p

Answer 1

Answer: (C)

p/2

Answer 2

Writing I

and using the given identity, we can write

I = $\int _ { 0 } ^ { \pi / 2 }$2[cos x + cos 3x + ......+ cos (2k –1) x] cos x dx

= $\int _ { 0 } ^ { \pi / 2 }$[(1 + cos 2x) + (cos 4x + cos 2x) + ..... +

(cos 2kx + cos (2k –2) x)] dx

=$\frac { \pi } { 2 }$