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

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

Verify

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

$$\frac{1}{2}-1^{2}=-\frac{1}{2}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1}{2}-1=-\frac{1}{2}$$

Subtract 1 from \frac{1}{2} to get -\frac{1}{2}.

$$-\frac{1}{2}=-\frac{1}{2}$$

Compare -\frac{1}{2} and -\frac{1}{2}.

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