If x- tan22-5- - then the value of x4 - 3x3 -3x2-9x-6 is

Given : x= tan(22.5)^∘ Now, nbsp;tan 45^∘=2x1 x^2 ⇒ 1 x^2 =2x ⇒ x^2 +2x 1=0 Given expression is x^4 + 3x^3 3x^2 9x+6 =(x^2+x 4)(x^2+2x 1)+2 =0+2=2 ...

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Byju's Answer

Standard XIII

Mathematics

Trigonometric Ratios of Multiple Angles: sin2θ ; cos2θ ; tan2θ

If x= tan22.5...

Question

If $x = tan (22.5)^{\circ},$ then the value of $x^{4} + 3 x^{3} - 3 x^{2} - 9 x + 6$ is

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Solution

Given : $x = tan (22.5)^{\circ}$
Now, $tan 45^{\circ} = \frac{2 x}{1 - x^{2}}$
$\Rightarrow 1 - x^{2} = 2 x \Rightarrow x^{2} + 2 x - 1 = 0$
Given expression is
$x^{4} + 3 x^{3} - 3 x^{2} - 9 x + 6 = (x^{2} + x - 4) (x^{2} + 2 x - 1) + 2 = 0 + 2 = 2$

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If x=tan(22.5)∘, then the value of x4+3x3−3x2−9x+6 is

Given : x=tan(22.5)∘ Now, tan45∘=2x1−x2 ⇒1−x2=2x⇒x2+2x−1=0 Given expression is x4+3x3−3x2−9x+6=(x2+x−4)(x2+2x−1)+2=0+2=2

If $x = tan (22.5)^{\circ},$ then the value of $x^{4} + 3 x^{3} - 3 x^{2} - 9 x + 6$ is

Given : $x = tan (22.5)^{\circ}$
Now, $tan 45^{\circ} = \frac{2 x}{1 - x^{2}}$
$\Rightarrow 1 - x^{2} = 2 x \Rightarrow x^{2} + 2 x - 1 = 0$
Given expression is
$x^{4} + 3 x^{3} - 3 x^{2} - 9 x + 6 = (x^{2} + x - 4) (x^{2} + 2 x - 1) + 2 = 0 + 2 = 2$