Explanation Theorem Used: Pythagorean Theorem: In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. Result used: The Basic Trigonometric Identity: cos ( 2 θ ) = 2 cos 2 θ − 1 . Calculation: Consider the given expression cos ( 2 tan − 1 x ) . cos ( 2 tan − 1 x ) = cos ( 2 θ ) where, θ = tan − 1 x . By Pythagorean Theorem third side of the triangle is as follows, ( Hypotenuse ) 2 = 1 2 + x 2 = 1 + x 2 Hypotenuse = 1 + x 2 Draw a right angle by using tan θ = x 1 as shown in below Figure1, From Figure 1, it is observed that 1 + x 2 represents hypotenuse of the triangle, 1 and x are two legs of the triangle. Now, find the value of cos ( 2 θ ) using the formula stated above

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Chapter 20.6, Problem 50E

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To find: The value of the expression cos(2tan−1x).

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Chapter 20.6, Problem 49E

Chapter 20.6, Problem 51E

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2 Q/ Let d₂ +d, di, d2: R² XR² R² defined as follow ((x+x), (2, 1) = √(x-2)² + (x_wx • d₁ ((x,y), (z, w)) = max {1x-z\, \y-w\} • 1 1 dq ((x,y), (Z, W)) = \ x=2\+\-w| 2 • show that dod₁, d₂ are equivalent? 2

2 +d, di, d2: R² XR² > R² defined as follow Q/ Let d₂ 2/ d((x+x), (2, 1)) = √(x-2)² + (x-wsc • d₁ ((x,y), (z, w)) = max {| x-z\, \y-w\} • d₂ ((x, y), (Z, W)) = 1x-21+ \y-w| 2 • show that ddi, d₂ are equivalent? އ

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Chapter 20 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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The value of the expression cos ( 2 tan − 1 x ) .

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To find: The value of the expression cos(2tan−1x).

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