Find all solutions to tan ⁡ ( x − π ) + 2 sin ⁡...

neudateaLp

neudateaLp

Answered

2022-11-25

Find all solutions to tan ( x π ) + 2 sin ( x π ) = 0 on [ 0 , 2 π )

Answer & Explanation

ysik92ASw

ysik92ASw

Expert

2022-11-26Added 13 answers

Given
tan ( x π ) + 2 sin ( x π ) = 0
We know that
sin ( x π ) cos ( x π ) + 2 sin ( x π ) = 0 sin ( x π ) [ 1 cos ( x π ) + 2 ] = 0 If  sin ( x π ) = 0 x π = sin 1 ( 0 ) = 0 x = π
If 1 cos ( x π ) + 2 = 0 1 cos ( x π ) = 2 cos ( x π ) = 1 2 x π = cos 1 ( 1 2 ) x π = 60 x = 240 x = 4 π 3

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