Home
Class 12
MATHS
Let P(k)=(1+cospi/(4k)) (1+cos((2k-1)pi)...

Let `P(k)=(1+cospi/(4k))` `(1+cos((2k-1)pi)/(4k))` `(1+cos((2k+1)pi)/(4k))(1+cos((4k-1)pi)/(4k))dotT h e n` `P(3)=1/(16)` (b) `P(4)=(2-sqrt(2))/(16)` `P(5)=(3-sqrt(5))/(32)` (d) `P(6)(2-sqrt(3))/(16)`

Text Solution

Verified by Experts

The correct Answer is:
`(3-sqrt(5))/(32)` (b) `(2-sqrt(3))/(16)`
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Let P(k)=(1+cos((pi)/(4k)))(1+cos(((2k-1)pi)/(4k)))(1+cos(((2k+1)pi)/(4k)))(1+cos(((4k-1)pi)/(4k))) Then (a)P(3)=(1)/(16) (b) P(4)=(2-sqrt(3))/(16)P(5)=(3-sqrt(5))/(32)( d) P(6)(2-sqrt(3))/(16)

Let F(x)=(1+sin((pi)/(2k))(1+sin(k-1)(pi)/(2k))(1+sin(2k+1)(pi)/(2k))(1+sin(3k-1)(pi)/(2k)) The value of F(1)+F(2)+F(3) is equal to

sum_(m=1)^(4n+1)[sum_(K=1)^(m-1){sin((2k pi)/(m))-i cos((2k pi)/(m))}^(m)]

If (3-tan^(2)((pi)/(7)))/(1-tan^(2)((pi)/(7)))=k cos((pi)/(7)) then the value 1-tan^(2)((pi)/(7)) of k is (a) (b)2(c)3(d)4

If z_(k)=cos((k pi)/(10))+i sin((k pi)/(10)), then z_(1)z_(2)z_(3)z_(4) is equal to (A)-1 (B) 2(C)-2 (D) 1

If cos^(-1)sqrt(p)+cos^(-1)sqrt(1-p)+cos^(-1)sqrt(1-q)=(3pi)/(4)"than :"q=

sum_(m=1)^(32)m[sum_(k=1)^(6)sin2k(pi)/(7)-i cos2k(pi)/(7)]

The value of sin^(-1)((3)/(sqrt(73)))+cos^(-1)((11)/(sqrt(146)))+cot^(-1)sqrt(3) is k pi then (1)/(k)

16 * cos ""(pi)/(12) * cos"" (4pi)/(12) * cos"" (5pi)/(12)= A) sqrt1 B) sqrt2 C) sqrt3 D) sqrt4