Question

Which expression is equivalent to Tangent (3pi/4-2x)

A.-1-tan(2x)/1-(-1)(tan(2x))
B..-1-tan(2x)/1+(-1)(tan(2x))
C.1-tan(2x)/1+(1)(tan(2x))
D.1+tan(2x)/1-(1)(tan(2x))

Answer 1

The expression equivalent to tangent (3π/4 - 2x) is A. -1 - tan(2x)/1 - (-1)(tan(2x)).

Step-by-step explanation:

The expression equivalent to tangent (3π/4 - 2x) is A. -1 - tan(2x)/1 - (-1)(tan(2x)).

To confirm this, we can use the trigonometric identity for tangent subtraction:
tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b))

In this case, a = 3π/4 and b = 2x.

Substituting these values into the identity, we get:
tan(3π/4 - 2x) = (tan(3π/4) - tan(2x))/(1 + tan(3π/4)tan(2x))

Simplifying further, we have:
= (-1 - tan(2x))/(1 - (-1)(tan(2x)))

Therefore, the equivalent expression is A. -1 - tan(2x)/1 - (-1)(tan(2x)).