Question

what is the exact value of sin^2(13pi/5)+cos^2(13pi/5) and explain

Answer 1

There's a trigonometry identity that sin^2(x)+cos^2(x)=1, hence if x=13pi/5;
sin^2(13pi/5)+cos^2(13pi/5)=1

Answer 2

One way to see this is with a right triangle with hypotenuse one:

Answer 3

thanks . can you also help me with 2cos^2(pi/8)-1

Answer 4

OK, \[\sin^{2}(x)+\cos^{2}(x)=1\] double
\[2\sin^{2}(x)+2\cos^{2}(x)=2\] subtract 1 from each side
\[2\sin^{2}(x)+2\cos^{2}(x)-1=1\]
Now do you see your equation in the middle? Simplify for your answer.