if sin25=a and cos40=b, express cos140 / (tan205) (cos385) in terms of a and b

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if sin25=a and cos40=b, express cos140 / (tan205) (cos385) in terms of a and b

Mathematics
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Is it \( \large { \cos140^\circ} \over { (\tan 205^\circ) (\cos 385^\circ)} \) ?
ys
We have \[\frac{cos 140}{tan 205 * cos 385}\] tan (205)=tan(180+25)= tan (25) =\(\frac{sin 25}{cos 25}\) cos 140= cos(180-40)= - cos 40 cos 385=cos(360+25)=cos 25 substituting these in the given expression \[\frac{-\cos 40}{\frac{sin 25}{cos 25} * cos 25}\] now we cancel the cos 25 \[\frac{-\cos 40}{\frac{sin 25}{\cancel{cos 25}} * \cancel{cos 25}}\] we have now \[\frac{-\cos 40}{\sin25}\] so we get \[\frac{-b}{a}\]

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Other answers:

cos 140 = -cos 40 tan205=tan25 cos385=cos25 \[\frac{-\cos40}{\frac{\sin25}{\cos25}\cos25}\]
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welcome lovampire_lsc, Did you understand the solution?
ys, super clearly thanks a lot

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