Respuesta :
Answer:
True.
Step-by-step explanation:
Given : [tex]tan\,(\frac{\pi}{2}-x)=cot\,x[/tex]
We know complementary function in trigonometry is given as follows
sin (90 - x ) = cos x
sin changes into cos , cos changes into sin
tan changes into cot and cot changes into tan
sec changes into cosec and cosec changes into sec.
But sign depends on quadrant in which it going to belong
like cos ( 90 - x ) = sin x as 90 - x belong to 1st quadrant in which cos gives positive value.
while cos ( 90 + x ) = -sin x as 90 + x belong to 2nd quadrant in which cos gives negative value.
Similarly for tan ( 90 - x ) = cot x as it belong in 1st quadrant and in 1st quadrant tan is positive.
therefore, Answer is True.
