Q. Prove that: (cos40 – sin40)/(cos40 + sin40) = tan5

Soln:

RHS

= tan5

= tan(45 – 40)                                 

= (tan45 – tan40)/(1 + tan45.tan40)            [tan(A-B) = (tanA-tanB)/(1+tanA.tanB)]

= (1 – tan40)/(1 + 1.tan40)

= (1 – sin40/cos40)/(1 + sin40/cos40)

= [(cos40 – sin40)/cos40]/[(cos40 + sin40)/cos40]

= (cos40 – sin40)/(cos40 + sin40)