4 cot square - sec square 60 + sin square 60 +cos square 60 = 1

Question

verify the following equalities

Answer 1

sin(60)=√3/2, cos(60)=1/2, tan(60)=√3,

sec(60)=2, cot(60)=√3/3.

So, 4/3-4+3/4+1/4=-8/3.

sin²(x)+cos²(x)=1 for all x, therefore 4cot²(60)-sec²(60) has to equal zero. But 4cot²(x)=sec²(x), 4cos²(x)=tan²(x) when 4cos⁴(x)=sin²(x)=1-cos²(x). So, 4cos⁴(x)+cos²(x)-1=0, cos²(x)=(-1+√(1+16))/8 (negative value is rejected), cos²(x)=(√17-1)/8=0.39039 approx. cos(x)=0.6248, x=51.33°, not 60°.