Special types of equations

JEE Main Mathematics · Trigonometric Equations · 2 questions, latest first

• The number of elements in the set {x ∈[0,180^°]: tan (x+100^°)= tan (x+50^°) tan x tan (x-50^°)} is ____.202624 January, Shift 2 · Q24
• Let S={x ∈(-(π)/2, (π)/2): 9^1- tan^2 x+9^tan^2 x=10} and β=Σ_x ∈ s tan^2(x/3), then 1/6(β-14)^2 is equal to202310 April, Shift 2 · Q2