given that sec 60 degree=2 find the sec 20 degree without using a calculator..i know this is easy question,but i dont know how to get the answer..please help!
this reply is a bit late but you might still be interested to know the solution and it's not easy .
sec 60 =2
cos 60=1/2
Do you know the triple angle formula ,
cos 3x =4cos^3 x -3cos x
Substitute x=20 ,
cos 3(20)=4cos^3 20- 3cos 20
1/2=4cos^3 20-3 cos 20
8cos^3 20-6cos 20-1=0
Solving this ,
cos 20 = 0.94 , cos 20= -0.77(undefined) , cos 20 = -0.17 (undefined) --- since cos cant be -ve in the 1st quadrant
sec 20 = 1/0.94
sec 20 = 1.064