Question

tan(2019pi- x)=......​

Answer 1

We know that,

tan ( n. π + θ) = ± tanθ and, sign is decided by where the angle lies.

2019 π - x lies in third quadrant.

( 2019 π - x can be written as (504 * 4 + 3)π - x

So, The given angle lies in third quadrant.

We know that,

ALL SILVER TEA CUPS

ALL - All trigonometric ratios are positive in First quadrant.

SILVER - Sine and it's reciprocal are positive in second quadrant.

TEA - tangent and it's reciprocal are positive in third quadrant.

CUPS - cosine and it's reciprocal are positive in fourth quadrant.

So, In third quadrant, Tangent is positive.

tan ( n. π + θ) = + tanθ,

Final we get,

tan ( 2019 π - x) = tan x