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`        (1+cosπ/8)( 1+cos3π/8)(1+cod 5π/8)(1+cos7π/8) prove that it is1/2`
10 months ago

Arun
22998 Points
```							cos 5pi/8=cos(pi/2+pi/8)=-sin pi/8cos 3pi/8=cos(pi/2-pi/8)=sin pi/8cos 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
```
10 months ago
Narendra Beniwal
34 Points
```							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
```
10 months ago
Narendra Beniwal
34 Points
```							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
```
10 months ago
Arun
22998 Points
```							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
```
10 months ago
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### Course Features

• 31 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions