Simplify the given expression:
If f(x)=∣∣ ∣∣sin xsin asin bcos xcos acos btan xtan atan b∣∣ ∣∣,
where 0<a<b<π2 then the equation f′(x)=0 has in the interval (a,b)
acosφ=bcosθ
Show that
atanθ+btanφ=(a+b) tan (θ+φ) ÷2