SOLUTION: sin10°cot 20°cos 30°tan40°tan50°cosec 60°cot70°sec 80°=1 prove.

Algebra ->  Trigonometry-basics -> SOLUTION: sin10°cot 20°cos 30°tan40°tan50°cosec 60°cot70°sec 80°=1 prove.      Log On


   

Question 1078890: sin10°cot 20°cos 30°tan40°tan50°cosec 60°cot70°sec 80°=1 prove.
Answer by ikleyn(52864) About Me  (Show Source):
You can put this solution on YOUR website!
.
sin10°cot 20°cos 30°tan40°tan50°cosec 60°cot70°sec 80°=1 prove.
~~~~~~~~~~~~~~~~

Use basic trigonometry identities: 

1.  sin(10°) = cos(80°) = 1%2Fsec%2880%5Eo%29   --->  sin(10°)*sec(80°) = 1.


2.  cot(20°) = 1%2Fcot%2870%5Eo%29   --->  cot(20°)*cot(70°) = 1.


3.  cos(30°) = sin(60°) = 1%2Fcosec%2860%5Eo%29   --->  cos(30°)*cosec(60°) = 1.


4.  tan(40°) = 1%2Ftan%2850%5Eo%29   --->  tan(40°)*tan(50°) = 1.



5.  =======>  sin10°cot 20°cos 30°tan40°tan50°cosec 60°cot70°sec 80° = 1.   Proved.