Trigonometry

Identities, equations, and angle relationships.

  1. Given that A= (sin 6°)/(cos 18°) B = (sin 12°)/(cos 36°) C= (sin 18°)/(cos 54°) and P= tan 18° cos 12°- sin 12° Q= tan 36° cos 24°- sin 24° R= tan 54° cos 36°+ sin 36° then find the value of N= (A/P + B/Q + C/R)²+ A/P + B/Q + C/R
  2. If cos² [ π/4 (sin x + √2 cos² x) ] - tan² (x + π/4 tan² x) = 1 then find the value of sin (x).
  3. If (tan 70° tan 10°+3)/(tan 70°+ tan 10°) = tan x and x is acute, then find x.