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 23E
To determine

To prove:

  sinθcotθ=cosθ

Expert Solution

Explanation of Solution

Given information:

Eq: sinθcotθ=cosθ

Formula Used:

  cotθ=1tanθ

Proof:

The equation is given as:

  sinθcotθ=cosθ

The left hand side of the eq. which should be give result as right hand side:

  sinθcotθ=sinθ×1tanθsinθcotθ=sinθ×1(sinθcosθ)[tanθ=sinθcosθ]sinθcotθ=sinθ×cosθsinθsinθcotθ=cosθ

So, sinθcotθ=cosθ is an identity for all values of θ

Hence, proved.

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