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if x=22°3`,then (1+cosx)(1+cos3x)(1+cos5x)(1+cos7x)equals

if x=22°3`,then (1+cosx)(1+cos3x)(1+cos5x)(1+cos7x)equals

Grade:11

2 Answers

Aditya Gupta
2081 Points
4 years ago
x=π/8
so, Z=(1+cosx)(1+cos3x)(1+cos5x)(1+cos7x)=(1+cosπ/8)(1+cos3π/8)(1 – cos3π/8)(1 – cosπ/8) [using cosy= – cos(π-y)]
implies Z= (1 – cos^2(3π/8))(1 – cos^2(π/8))=sin^2(π/8)*sin^2(3π/8)=(1 – cos(π/4))(1 – cos(3π/4))/4 [using cos2t=1 – sin^2t)
so Z= (1 – cos(π/4))(1 + cos(π/4))/4=sin^2(π/4)/4= 1/8
Aman Dubey
13 Points
one year ago
(1+cos(pi/8)) (1+cos(pi/2-3pi/8)) (1+cos(pi/2-5pi/8)) (1+cos(pi-7pi/8))
(1+cos pi/8) (1+sin pi/8) (1-sin pi/8) (1-cos pi/8)
(1-cos^2 pi/8) ( 1-sin^2 pi/8)
sin^2 (pi/8) cos^2 (pi/8)
¼(2sin(pi/8)cos(pi/8))^2
¼ sin^2 (2pi/8)
¼ sin^2(pi/4)
¼(1/root2)^2
1/8

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