Solve {left(sin(35)/cos(55)right)}^2+{left(cos(55)/sin(35)right)}^2-2cos(60)

$${ \left( \frac{ \sin ( 35 ) }{ \cos ( 55 ) } \right) }^{ 2 } + { \left( \frac{ \cos ( 55 ) }{ \sin ( 35 ) } \right) }^{ 2 } -2 \cos ( 60 )$$

Evaluate

$$1$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(\frac{0.573576436351046}{0.573576436351046})} ^ {2} + {(\frac{0.573576436351046}{0.573576436351046})} ^ {2} - 2 \cos(60)$$

Divide 0.573576436351046 by 0.573576436351046 to get 1.

$$1^{2}+\left(\frac{0.573576436351046}{0.573576436351046}\right)^{2}-2\cos(60)$$

Divide 0.573576436351046 by 0.573576436351046 to get 1.

$$1^{2}+1^{2}-2\cos(60)$$

Calculate 1 to the power of 2 and get 1.

$$1+1^{2}-2\cos(60)$$

Calculate 1 to the power of 2 and get 1.

$$1+1-2\cos(60)$$

Add 1 and 1 to get 2.

$$2-2\cos(60)$$

Get the value of \cos(60) from trigonometric values table.

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

Multiply 2 and \frac{1}{2} to get 1.

$$2-1$$

Subtract 1 from 2 to get 1.

$$1$$