BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter C, Problem 25E
To determine

To prove:

  tan2θ=2tanθ1tan2θ

Expert Solution

Explanation of Solution

Given information:

Eq: tan2θ=2tanθ1tan2θ

Formula Used:

Addition formula for tangent:

  tan(x+y)=tanx+tany1tanxtany

Proof:

The equation is given as:

  tan2θ=2tanθ1tan2θ

The left hand side of the eq.:

  tan2θ=tan(θ+θ)tan2θ=tanθ+tanθ1tanθtanθtan2θ=2tanθ1tan2θ

Since, left hand side (tan2θ) equals to right hand side (2tanθ1tan2θ) for all values θ . So, tan2θ=2tanθ1tan2θ is an identity.

Hence, proved.

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