## anonymous 4 years ago if sin25=a and cos40=b, express cos140 / (tan205) (cos385) in terms of a and b

1. anonymous

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

2. anonymous

ys

3. ash2326

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 $\frac{-b}{a}$

4. Mertsj

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

5. anonymous

thx=]

6. ash2326

welcome lovampire_lsc, Did you understand the solution?

7. anonymous

ys, super clearly thanks a lot