Question

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

Answer 1

Is it \( \large { \cos140^\circ} \over { (\tan 205^\circ) (\cos 385^\circ)} \) ?

Answer 2

ys

Answer 3

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
\[\frac{-b}{a}\]

Answer 4

cos 140 = -cos 40
tan205=tan25
cos385=cos25
\[\frac{-\cos40}{\frac{\sin25}{\cos25}\cos25}\]

Answer 5

thx=]

Answer 6

welcome lovampire_lsc, Did you understand the solution?

Answer 7

ys, super clearly thanks a lot