What is the value of 2/(2+cos(270)) ?

The value of 2/(2+cos(270)) is 1

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2/(2+cos(270))

\frac{2}{2 + cos ( 27 0 ^{\circ} )}

1

Solution steps

\frac{2}{2 + cos ( 27 0 ^{\circ} )}

Rewrite using trig identities:

cos (27 0^{\circ}) = cos^{2} (13 5^{\circ}) - sin^{2} (13 5^{\circ})

= \frac{2}{2 + cos ^{2} ( 13 5 ^{\circ} ) - sin ^{2} ( 13 5 ^{\circ} )}

Use the following trivial identity:

cos (13 5^{\circ}) = - \frac{2}{2}

Use the following trivial identity:

sin (13 5^{\circ}) = \frac{2}{2}

= \frac{2}{2 + ( - \frac{2}{2} ) ^{2} - ( \frac{2}{2} ) ^{2}}

Simplify

\frac{2}{2 + ( - \frac{2}{2} ) ^{2} - ( \frac{2}{2} ) ^{2}} : 1

= 1

sin (\frac{7}{12})

arccot (cot (- 1 0^{\circ}))

2 sin (- 7 0^{\circ})

cos (6 0^{\circ}) cos (6 5^{\circ}) - sin (6 0^{\circ}) sin (6 5^{\circ})

arcsin (\frac{0}{3})