Question

tan( 3π/4. + x ) = ___ options are
A) – tan(π/4 – x) B) tan(π/4 – x) C) tan(π/4+x) D)-tan(π/4+x)​

Answer 1

Answer:

(d) -tan(π/4+x)

Step-by-step explanation:

3π/4=π-π/4

tan(3π/4+x)= tan(π-π/4+x)

=-tan(π/4+x)

because tan is negative in second quadrant.

Answer 2

Given,

A trigonometric expression: Tan (3π/4 + x)

To find,

The value of the given trigonometric expression.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically, according to the trigonometric identities;

If x is any angle, then,

Tan (π-x) = -Tan x

{Statement-1}

Now, using the statement-1 in the given trigonometric expression, we get;

Tan (3π/4 + x)

= Tan (π - π/4 + x)

= Tan {π - (π/4-x)}

= -Tan (π/4-x)

Hence, the value of the given trigonometric expression is equal to -Tan (π/4-x). (Option-A)