Question

simplifica M= (1-sen² x) (1+ctg² x). tag x

Answer 1

Recordemos:

• 1 - sen²x = cos²x
• 1 + cot²x = csc²x

Procedimiento:

${(1-\sin^2x)(1+\cot^2x).\tan x=}\\\\{\cos^2x.\csc^2x.\tan x=}\\\\\\{\dfrac{\cos^2 x}{1}\ .\ \dfrac{1}{\sin ^2x}\ .\ \dfrac{\sin x}{\cos x}=}\\\\\\{\dfrac{\cos x}{\sin x}=}\\\\\\{\boxed{\cot x}}$