What is the value of sqrt((1+cos(20))/2)-cos(10) ?

The value of sqrt((1+cos(20))/2)-cos(10) is 0

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sqrt((1+cos(20))/2)-cos(10)

\frac{1 + cos ( 2 0 ^{\circ} )}{2} - cos (1 0^{\circ})

0

Solution steps

\frac{1 + cos ( 2 0 ^{\circ} )}{2} - cos (1 0^{\circ})

Rewrite using trig identities:

cos (2 0^{\circ}) = 2 cos^{2} (1 0^{\circ}) - 1

cos (2 0^{\circ})

Write

cos (2 0^{\circ})

cos (2 \cdot 1 0^{\circ})

= cos (2 \cdot 1 0^{\circ})

Use the Double Angle identity:

cos (2 x) = 2 cos^{2} (x) - 1

= 2 cos^{2} (1 0^{\circ}) - 1

= \frac{1 + 2 cos ^{2} ( 1 0 ^{\circ} ) - 1}{2} - cos (1 0^{\circ})

Simplify

= 0

(\frac{25 \cdot 32}{23} \cdot tan (60. 9^{\circ})) - 25

sin (- 1 (\frac{4}{5}))

tan (1 0^{\circ}) cot (1 0^{\circ})

9 sin (\frac{π}{4})

\frac{25}{sin ( 3 0 ^{\circ} )}

What is the value of sqrt((1+cos(20))/2)-cos(10) ?
The value of sqrt((1+cos(20))/2)-cos(10) is 0