Question

Prove that tanx +cotx=2cosec2x and deduce that 75°+cot75°=4

Answer 1

Answer:

Step-by-step explanation:

tanx +cotx=2cosec2x

L.H.S:

Sinx/Cos + Cosx/Sinx

= Sin²x + Cos²x/sinxcosx

= 1/sinxcosx

= 1/(1/2)sin2x

= 2/sin2x

= 2cosec2x

= R.H.S

Now Tan75° + Cot 75° = 2/Sin150°

                                      = 2/Cos60°

                                      = 2/(1/2)

                                      = 4.