What is the value of 1/(cos(33)cos(12)-sin(33)sin(12)) ?

The value of 1/(cos(33)cos(12)-sin(33)sin(12)) is square root of 2

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1/(cos(33)cos(12)-sin(33)sin(12))

\frac{1}{cos ( 3 3 ^{\circ} ) cos ( 1 2 ^{\circ} ) - sin ( 3 3 ^{\circ} ) sin ( 1 2 ^{\circ} )}

2

Solution steps

\frac{1}{cos ( 3 3 ^{\circ} ) cos ( 1 2 ^{\circ} ) - sin ( 3 3 ^{\circ} ) sin ( 1 2 ^{\circ} )}

Rewrite using trig identities:

cos (3 3^{\circ}) cos (1 2^{\circ}) - sin (3 3^{\circ}) sin (1 2^{\circ}) = cos (4 5^{\circ})

= \frac{1}{cos ( 4 5 ^{\circ} )}

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

= \frac{1}{\frac{2}{2}}

Simplify

\frac{1}{\frac{2}{2}} : 2

= 2

arcsin (\frac{19}{32})

arcsin (cos (\frac{π}{2}))

cos^{2} (33 0^{\circ})

arctan (\frac{12}{4})

arctan (\frac{- 3}{3})

What is the value of 1/(cos(33)cos(12)-sin(33)sin(12)) ?
The value of 1/(cos(33)cos(12)-sin(33)sin(12)) is square root of 2