if tan x = 1 , then the value of 2 sin x + sin ( π + x) + cos ( π – x) is equal to?

Answer 1

tan(x) = 1
2sin(x) + sin(pi + x) + cos(pi - x) = ?

One way to solve is to just solve for x; we'll get an infinite number of solutions, but let's assume the definition of arctan, which uses the interval from -pi/2 to pi/2.

If tan(x) = 1, then x = arctan(1) = pi/4.

2sin(pi/4) + sin(pi + pi/4) + cos(pi - pi/4) =

2(sqrt(2)/2) + sin(5pi/4) + cos(3pi/4) =

sqrt(2) + (-sqrt(2)/2) + (-sqrt(2)/2) =

sqrt(2) + (-2sqrt(2)/2) =

sqrt(2) + (-sqrt(2)) = 0

Answer 2

sin ( π + x) = -sin(x)
cos( π - x) = -cos(x)

2sin(x) - sin(x) -cos(x) = sin(x) - cos(x)

factor out cos(x):

cos(x)[ sin(x)/cos(x) - 1] and since sin(x)/cos(x) = tan(x)

cos(x)[tan(x) - 1]

and we are told that tan(x) = 1

cos(x)[ 1 -1] =0

so under these conditions:

if tan(x) =1
then 2 sin x + sin ( π + x) + cos ( π – x) = 0

Answer 3

if tanx=1 x is 45 degrees.
substitute it in the second equation to get the solution.