oliver incorrectly states that the expression \\( \\tan \\left( \\frac { 3 \\pi } { 4 } + x \\right) \\) can…

oliver incorrectly states that the expression \\( \\tan \\left( \\frac { 3 \\pi } { 4 } + x \\right) \\) can be simplified as -1. review olivers work. \\( \\tan \\left( \\frac { 3 \\pi } { 4 } + x \\right) \\) \\( = \\frac { \\tan \\left( \\frac { 3 \\pi } { 4 } \\right) + \\tan ( x ) } { 1 - \\tan \\left( \\frac { 3 \\pi } { 4 } \\right) \\tan ( x ) } \\) \\( = \\frac { - 1 + \\tan ( x ) } { 1 - ( - 1 ) \\tan ( x ) } \\) \\( = \\frac { - 1 + \\tan ( x ) } { 1 + \\tan ( x ) } \\) \\( = - 1 \\) which statement explains why oliver is incorrect \\( \\bigcirc \\) the expression \\( \\frac { - 1 + \\tan ( x ) } { 1 + \\tan ( x ) } \\) does not simplify to -1. \\( \\bigcirc \\) the expression \\( \\tan \\left( \\frac { 3 \\pi } { 4 } \\right) \\) does not have a value of -1. \\( \\bigcirc \\) the expression \\( 1 - ( - 1 ) \\tan ( x ) \\) simplifies to \\( 2 \\tan ( x ) \\), not \\( 1 + \\tan ( x ) \\). \\( \\bigcirc \\) the expression \\( \\tan \\left( \\frac { 3 \\pi } { 4 } + x \\right) \\) is equivalent to \\( \\tan \\left( \\frac { 3 \\pi } { 4 } \\right) + \\tan ( x ) \\), not \\( \\frac { \\tan \\left( \\frac { 3 \\pi } { 4 } \\right) + \\tan ( x ) } { 1 - \\tan \\left( \\frac { 3 \\pi } { 4 } \\right) \\tan ( x ) } \\)

oliver incorrectly states that the expression \\( \\tan \\left( \\frac { 3 \\pi } { 4 } + x \\right) \\) can be simplified as -1. review olivers work. \\( \\tan \\left( \\frac { 3 \\pi } { 4 } + x \\right) \\) \\( = \\frac { \\tan \\left( \\frac { 3 \\pi } { 4 } \\right) + \\tan ( x ) } { 1 - \\tan \\left( \\frac { 3 \\pi } { 4 } \\right) \\tan ( x ) } \\) \\( = \\frac { - 1 + \\tan ( x ) } { 1 - ( - 1 ) \\tan ( x ) } \\) \\( = \\frac { - 1 + \\tan ( x ) } { 1 + \\tan ( x ) } \\) \\( = - 1 \\) which statement explains why oliver is incorrect \\( \\bigcirc \\) the expression \\( \\frac { - 1 + \\tan ( x ) } { 1 + \\tan ( x ) } \\) does not simplify to -1. \\( \\bigcirc \\) the expression \\( \\tan \\left( \\frac { 3 \\pi } { 4 } \\right) \\) does not have a value of -1. \\( \\bigcirc \\) the expression \\( 1 - ( - 1 ) \\tan ( x ) \\) simplifies to \\( 2 \\tan ( x ) \\), not \\( 1 + \\tan ( x ) \\). \\( \\bigcirc \\) the expression \\( \\tan \\left( \\frac { 3 \\pi } { 4 } + x \\right) \\) is equivalent to \\( \\tan \\left( \\frac { 3 \\pi } { 4 } \\right) + \\tan ( x ) \\), not \\( \\frac { \\tan \\left( \\frac { 3 \\pi } { 4 } \\right) + \\tan ( x ) } { 1 - \\tan \\left( \\frac { 3 \\pi } { 4 } \\right) \\tan ( x ) } \\)

Answer

Explanation:

Step1: Apply the tangent addition formula

The formula for (\tan(A + B)=\frac{\tan(A)+\tan(B)}{1-\tan(A)\tan(B)}). Here (A=\frac{3\pi}{4}) and (B = x), so (\tan(\frac{3\pi}{4}+x)=\frac{\tan(\frac{3\pi}{4})+\tan(x)}{1-\tan(\frac{3\pi}{4})\tan(x)}).

Step2: Calculate (\tan(\frac{3\pi}{4}))

We know that (\tan(\frac{3\pi}{4})=- 1). Substituting this value into the formula, we get (\frac{-1+\tan(x)}{1-(-1)\tan(x)}=\frac{-1+\tan(x)}{1 + \tan(x)}), which does not simplify to (-1).

Answer:

The expression (\frac{-1+\tan(x)}{1+\tan(x)}) does not simplify to (-1).