Trigonometry

Question

Prove that tanx = cotx - 2 cot 2x. Hence show that 2tan20º + 4tan40º + 8tan80º = 9(cot 10º-tan10º)

 

Thank You!:)

Answer 1

Begin with right side cotx - 2cot2x

=> cosx/sinx  - 2 cos2x/sin2x

Substitute sin2x = 2sinxcosx

=> cosx/sinx - 2cos2x/2sinxcosx

=> cosx/sinx - cos2x/sinxcosx

=> (cos²x - cos2x)/sinxcosx

substitute cos2x = cos²x - sin²x

=>( cos²x - cos²x + sin²x)/sinxcosx

=> sin²x/sinxcosx = sinx/cosx = tanx

:)