a-maths~~~~

a)L.H.S.=1+k
= 1+[cosβ/cos(2α+β)]
= [cos(2α+β)+cosβ]/cos(2α+β)
= [2cos[(2α+2β)/2]cos[(2α+β-β)/2]/cos(2α+β)
= [2cos(α+β)cosα]/ cos(2α+β)
= R.H.S.
b)L.H.S. = k-1
=[cosβ/cos(2α+β)]-1
= [cosβ- cos(2α+β)]/cos(2α+β)
= 2sin(α+β)sinα/ cos(2α+β)
R.H.S. = (k+1)tan(α+β)tanα
= [2cos(α+β)cosα]sin(α+β)sinα/ cos(2α+β)cos(α+β)cosα
= 2sin(α+β)sinα/ cos(2α+β)
= L.H.S.
c) tan5π/12=tan(π/4+π/6)
k-1=(k+1)tan(α+β)tanα
k-1=(k+1)tan(π/4+π/6)tan(π/4)
k-1=(k+1)tan(5π/12)/√3
tan(5π/12)=√3( k-1)/(k+1)
k=cos(π/6)/cos(π/2+π/6)
=(√3/2)/(-1/2)
= -√3
所以,
tan(5π/12)=√3(-√3-1)/( -√3+1)
=(-1-√3)/ ( -√3+1)
=(√3+1)/(√3-1)
=2+√3