Question

(1+tg^2x)cos^2x-(1+ctg^2x)sin^2x=2

Answer 1

$(1+ tg^2 x)\cdot \cos^2 x-(1+ ctg ^2 x)\cdot \sin^2x=2 \\ \\ \Big(1+\dfrac{\sin^2 x}{\cos^2 x}\Big) \cdot \cos^2 x - \Big(1+\dfrac{\cos^2x}{\sin^2x}\Big)\cdot \sin^2x = 2 \\ \\ \cos^2 x+ \sin^2x - \Big(\sin^2 x+\cos^2 x\Big) = 2 \\ \\ 1-1 = 2 \Rightarrow 0 = 2 (F) \Rightarrow \boxed{\boxed{x\in \emptyset}} \\ \\ \\ \boxed{\sin^2a+\cos^2a = 1}\rightarrow identitate$