Solve fsin^2pi/6+cos^2pi/3-tan^2pi/4=-1/2

$$f \sin ^ { 2 } \frac { \pi } { 6 } + \cos ^ { 2 } \frac { \pi } { 3 } - \tan ^ { 2 } \frac { \pi } { 4 } = - \frac { 1 } { 2 }$$

Solve for f

$$f=1$$

Steps for Solving Linear Equation

Get the value of \sin(\frac{\pi }{6}) from trigonometric values table.

$$f\times \left(\frac{1}{2}\right)^{2}+\left(\cos(\frac{\pi }{3})\right)^{2}-\left(\tan(\frac{\pi }{4})\right)^{2}=-\frac{1}{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$f\times \frac{1}{4}+\left(\cos(\frac{\pi }{3})\right)^{2}-\left(\tan(\frac{\pi }{4})\right)^{2}=-\frac{1}{2}$$

Get the value of \cos(\frac{\pi }{3}) from trigonometric values table.

$$f\times \frac{1}{4}+\left(\frac{1}{2}\right)^{2}-\left(\tan(\frac{\pi }{4})\right)^{2}=-\frac{1}{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$f\times \frac{1}{4}+\frac{1}{4}-\left(\tan(\frac{\pi }{4})\right)^{2}=-\frac{1}{2}$$

Get the value of \tan(\frac{\pi }{4}) from trigonometric values table.

$$f\times \frac{1}{4}+\frac{1}{4}-1^{2}=-\frac{1}{2}$$

Calculate 1 to the power of 2 and get 1.

$$f\times \frac{1}{4}+\frac{1}{4}-1=-\frac{1}{2}$$

Subtract 1 from \frac{1}{4} to get -\frac{3}{4}.

$$f\times \frac{1}{4}-\frac{3}{4}=-\frac{1}{2}$$

Add \frac{3}{4} to both sides.

$$f\times \frac{1}{4}=-\frac{1}{2}+\frac{3}{4}$$

Add -\frac{1}{2} and \frac{3}{4} to get \frac{1}{4}.

$$f\times \frac{1}{4}=\frac{1}{4}$$

Multiply both sides by 4, the reciprocal of \frac{1}{4}.

$$f=\frac{1}{4}\times 4$$

Multiply \frac{1}{4} and 4 to get 1.

$$f=1$$