(1+cosπ/8)( 1+cos3π/8)(1+cod 5π/8)(1+cos7π/8) prove that it is1/2
Penchala subbaiah , 6 Years ago
Grade 12
Trigonometry> (1+cosπ/8)( 1+cos3π/8)( 1+cod 5π/8)(1+cos...
5 AnswersArun
Last Activity: 6 Years ago
cos 5pi/8=cos(pi/2+pi/8)=-sin pi/8
cos 3pi/8=cos(pi/2-pi/8)=sin pi/8
cos 7pi/8=cos(pi-pi/8)=-cos pi/8. Now the expression (1+cos pi/8)(1+cos 3pi/8)(1+cos 5pi/8)(1+cos 7pi/8) can be written as,
(1+cos pi/8)(1+sin pi/8)(1-sin pi/8)(1-cos pi/8)
=[1-(cos pi/8)^2][1–(sin pi/8)^2]
=(sin pi/8)^2×(cos pi/8)^2
=1/4×(2 sin pi/8.cos pi/8)^2
=1/4(sin 2x pi/8)^2
=1/4(sin pi/4)^2
=1/4×1/[(2)^1/2]^2
=1/4×1/2
=1/8(proven)
Please check as answer is 1/8 . But you have given it 1/2
Narendra Beniwal
Last Activity: 6 Years ago
cos 5pi/8=cos(pi/2+pi/8)=-sin pi/8
cos 3pi/8=cos(pi/2-pi/8)=sin pi/8
cos 7pi/8=cos(pi-pi/8)=-cos pi/8. Now the expression (1+cos pi/8)(1+cos 3pi/8)(1+cos 5pi/8)(1+cos 7pi/8) can be written as,
(1+cos pi/8)(1+sin pi/8)(1-sin pi/8)(1-cos pi/8)
=[1-(cos pi/8)^2][1–(sin pi/8)^2]
=(sin pi/8)^2×(cos pi/8)^2
=1/4×(2 sin pi/8.cos pi/8)^2
=1/4(sin 2x pi/8)^2
=1/4(sin pi/4)^2
=1/4×1/[(2)^1/2]^2
=1/4×1/2
=1/8
Narendra Beniwal
Last Activity: 6 Years ago
cos 5pi/8=cos(pi/2+pi/8)=-sin pi/8
cos 3pi/8=cos(pi/2-pi/8)=sin pi/8
cos 7pi/8=cos(pi-pi/8)=-cos pi/8. Now the expression (1+cos pi/8)(1+cos 3pi/8)(1+cos 5pi/8)(1+cos 7pi/8) can be written as,
(1+cos pi/8)(1+sin pi/8)(1-sin pi/8)(1-cos pi/8)
=[1-(cos pi/8)^2][1–(sin pi/8)^2]
=(sin pi/8)^2×(cos pi/8)^2
=1/4×(2 sin pi/8.cos pi/8)^2
=1/4(sin 2x pi/8)^2
=1/4(sin pi/4)^2
= 1/4x(21/2) 2
= 1/2
Arun
Last Activity: 6 Years ago
Dear Narendra
sin pi/4 = 1/ sqrt(2)
you have commited a mistake in the second last line of above answer. Answer should be 1/8
Vishakha
Last Activity: 4 Years ago
Its correct this may be 1/7but it could hwhwhajwjjajqw qqkkwnwjwnqjam q wow qjqjqmam awbhqnq q q qnkq qjqjw jsnsjsisjmsmsmsksmksms snsksjnsjs snake so ssksmsjksks s s mskwmskskkkwkqnsnsjsk ajakmwmsmsmammss snskksmsmsmms
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