![Prove that: i) sin40^(@)cos50^(@)+cos40^(@)sin50^(@)=1 ii) cot(270^(@)-theta)cot(270^(@)+theta)(cot(540^(@)-theta)cot(540^(@)+theta)=1 iii) cospi/8+cos(3pi)/8+cos(5pi)/8+cos(7pi)/8=0 Prove that: i) sin40^(@)cos50^(@)+cos40^(@)sin50^(@)=1 ii) cot(270^(@)-theta)cot(270^(@)+theta)(cot(540^(@)-theta)cot(540^(@)+theta)=1 iii) cospi/8+cos(3pi)/8+cos(5pi)/8+cos(7pi)/8=0](https://d10lpgp6xz60nq.cloudfront.net/question-thumbnail/en_34798976.png)
Prove that: i) sin40^(@)cos50^(@)+cos40^(@)sin50^(@)=1 ii) cot(270^(@)-theta)cot(270^(@)+theta)(cot(540^(@)-theta)cot(540^(@)+theta)=1 iii) cospi/8+cos(3pi)/8+cos(5pi)/8+cos(7pi)/8=0
![What is the value of sin(10)cos(20)sin(30)cos(40)sin(50)cos(60)sin(70)cos(80)? Not in radians, in degrees. | Socratic What is the value of sin(10)cos(20)sin(30)cos(40)sin(50)cos(60)sin(70)cos(80)? Not in radians, in degrees. | Socratic](https://useruploads.socratic.org/IK25ycsASbety18tGT8x_New%20Doc%202018-01-06_1.jpg)
What is the value of sin(10)cos(20)sin(30)cos(40)sin(50)cos(60)sin(70)cos(80)? Not in radians, in degrees. | Socratic
![cos40° -sin40°)/(cos40°+sin40°) = tan5° | Prove | Trigonometric Ratios of Compound Angles | Trigonometry | Sci-Pi cos40° -sin40°)/(cos40°+sin40°) = tan5° | Prove | Trigonometric Ratios of Compound Angles | Trigonometry | Sci-Pi](https://1.bp.blogspot.com/-NEIBRACjLYM/XqmitO4YJOI/AAAAAAAAJRg/Uotx-8Sxrv0CM1JS6TuRu2y2vHne5MSqACLcBGAsYHQ/s1600/IMG_20200429_173359.png)
cos40° -sin40°)/(cos40°+sin40°) = tan5° | Prove | Trigonometric Ratios of Compound Angles | Trigonometry | Sci-Pi
![cos40° + sin40° = √2 cos5° | Prove | Trigonometric Ratios of Compound Angles | Trigonometry | Sci-Pi cos40° + sin40° = √2 cos5° | Prove | Trigonometric Ratios of Compound Angles | Trigonometry | Sci-Pi](https://1.bp.blogspot.com/-nfETtXitLjQ/Xpf5sl4HiWI/AAAAAAAAIm4/P-IsMtlsKUU6GD_vyvUrZre6RI7GCVUFQCLcBGAsYHQ/s1600/IMG_20200415_221612.png)