FAST IT IS TIMED WILL MARK BRAILIEST Oliver incorrectly states that the expression Tangent (StartFraction 3 pi Over 4 EndFraction + x) can be simplified as –1. Review Oliver’s work. Tangent (StartFraction 3 pi Over 4 EndFraction + x) Equals StartFraction tangent (three-fourths pi) + tangent (x) Over 1 minus tangent (three-fourths pi) tangent (x) EndFraction Equals StartFraction negative 1 + tangent (x) Over 1 minus (negative 1) tangent (x) EndFraction Equals StartFraction negative 1 + tangent (x) Over 1 + tangent (x) EndFraction = –1 Which statement explains why Oliver is incorrect The expression StartFraction negative 1 + tangent (x) Over 1 + tangent (x) EndFraction does not simplify to –1. The expression Tangent (three-fourths pi) does not have a value of –1. The expression 1 minus (negative 1) tangent (x) simplifies to 2 tangent (x), not 1 + tangent (x). The expression Tangent (Three-fourths pi + x) is equivalent to Tangent (three-fourths pi) + tangent (x), not StartFraction tangent (three-fourths pi) + tangent (x) Over 1 minus tangent (three-fourths pi) tangent (x) EndFraction.

Trigonometric equation is an equation involving one or more trigonometric ratios of unknown angles. It is expressed as ratios of sine(sin), cosine(cos), tangent(tan), cotangent(cot), secant(sec), cosecant(cosec) angles. For example, cos2 x + 5 sin x = 0 is a trigonometric equation.

According to the question

Oliver incorrectly states

Tangent (Start Fraction 3 pi Over 4 End Fraction + x) can be simplified as –1.

i,e

[tex]tan(\frac{3\pi }{4} +x ) = -1[/tex]

Solving the trigonometric equation

[tex]tan(\frac{3\pi }{4} +x )[/tex]

= [tex]\frac{tan(\frac{3\pi }{4})+tan (x )}{1-tan(\frac{3\pi }{4})tan (x )}[/tex]

As tan (3pi/4 ) = -1

Putting the value

= [tex]\frac{(-1)+tan (x )}{1-(-1)tan (x )}[/tex]

= [tex]\frac{(-1)+tan (x )}{1+tan (x )}[/tex] ≠ -1

This trigonometric equation cannot be equal to -1.

Hence, Oliver is incorrect because the expression Start Fraction negative 1 + tangent (x) Over 1 + tangent (x) End Fraction does not simplify to –1.

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