LHS=1/(cos290^@)+1/(sqrt3sin250^@)LHS=1cos290∘+1√3sin250∘
=1/(cos(360-70)^@)+1/(sqrt3sin(180+70)^@)=1cos(360−70)∘+1√3sin(180+70)∘
=1/(cos70^@)-1/(sqrt3sin70^@)=1cos70∘−1√3sin70∘
=(sqrt3sin70^@-cos70^@)/(sqrt3sin70^@cos70^@)=√3sin70∘−cos70∘√3sin70∘cos70∘
=1/sqrt3[(2{sqrt3sin70^@-cos70^@})/(2sin70^@cos70^@)]=1√3⎡⎢⎣2{√3sin70∘−cos70∘}2sin70∘cos70∘⎤⎥⎦
=1/sqrt3[(2*2{sin70^@*(sqrt3/2)-cos70^@*(1/2)})/(sin140^@)]=1√3⎡⎢
⎢⎣2⋅2{sin70∘⋅(√32)−cos70∘⋅(12)}sin140∘⎤⎥
⎥⎦
=1/sqrt3[(4{sin70^@*cos30^@-cos70^@*sin30^@})/(sin(180-40)^@)]=1√3[4{sin70∘⋅cos30∘−cos70∘⋅sin30∘}sin(180−40)∘]
=1/sqrt3[(4{sin(70-30)^@})/(sin40^@)]=1/sqrt3[(4{cancel(sin40^@)})/cancel((sin40^@))]=4/sqrt3=RHS
NOTE that cos(360-A)^@=cosA and sin(180+A)^@=-sinA