What is the value of (cos(326)}{cos(34)}+\frac{-5-sqrt(5))/8 ?

The value of (cos(326)}{cos(34)}+\frac{-5-sqrt(5))/8 is (3-sqrt(5))/8

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(cos(326)}{cos(34)}+\frac{-5-sqrt(5))/8

\frac{cos ( 32 6 ^{\circ} )}{cos ( 3 4 ^{\circ} )} + \frac{- 5 - 5}{8}

\frac{3 - 5}{8}

Decimal Notation

0.09549 \dots

Solution steps

\frac{cos ( 32 6 ^{\circ} )}{cos ( 3 4 ^{\circ} )} + \frac{- 5 - 5}{8}

Simplify

= \frac{8 cos ( 32 6 ^{\circ} ) + cos ( 3 4 ^{\circ} ) ( - 5 - 5 )}{8 cos ( 3 4 ^{\circ} )}

Rewrite using trig identities:

cos (32 6^{\circ}) = cos (3 4^{\circ})

cos (32 6^{\circ})

Use the following identity:

cos (x) = cos (36 0^{\circ} - x)

cos (x)

Use the following property:

cos (θ) = cos (- θ)

cos (x) = cos (- x)

= cos (- x)

Apply the periodicity of

cos

cos (36 0^{\circ} + θ) = cos (θ)

cos (- x) = cos (36 0^{\circ} - x)

= cos (36 0^{\circ} - x)

= cos (36 0^{\circ} - 32 6^{\circ})

Simplify

= cos (3 4^{\circ})

= \frac{8 cos ( 3 4 ^{\circ} ) + cos ( 3 4 ^{\circ} ) ( - 5 - 5 )}{8 cos ( 3 4 ^{\circ} )}

Simplify

= \frac{3 - 5}{8}

arctan (1.7)

4 sin^{2} (0)

sin (0.0001)

\frac{sin ( 0.0001 )}{0.0001}

cot (arctan (3))

What is the value of (cos(326)}{cos(34)}+\frac{-5-sqrt(5))/8 ?
The value of (cos(326)}{cos(34)}+\frac{-5-sqrt(5))/8 is (3-sqrt(5))/8