Solve zeta-x^2=2cos15^circ

$$\zeta - x ^ { 2 } = 2 \cos 15 ^ { \circ }$$

Solve for ζ

$$\zeta =x^{2}+1.9318516525781366$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\zeta - x ^ {2} = 2 \cdot 0.9659258262890683$$

Multiply 2 and 0.9659258262890683 to get 1.9318516525781366.

$$\zeta -x^{2}=1.9318516525781366$$

Add x^{2} to both sides.

$$\zeta =1.9318516525781366+x^{2}$$

Solve for x

$$x=\frac{\sqrt{4\zeta -7.7274066103125464}}{2}$$

$$x=-\frac{\sqrt{4\zeta -7.7274066103125464}}{2}\text{, }\zeta \geq \frac{9659258262890683}{5000000000000000}$$