Chapter 6: Q. 10 (page 435)

Find the exact value of each expression. Do not use a calculator.
$\cos 540^{\circ} - \tan (- 405^{\circ})$

Short Answer

Expert verified

The value of the given expression is 0.

Step by step solution

Step 1. Given

Given trigonometric function

$\cos 540^{\circ} - \tan (- 405^{\circ})$

Step 2. Concept

We will use standard formula of $\sin θ$ and $\cos θ$ at different angles for calculating the final result of given expression.

Step 3. Calculation of cos540∘

We know

$\cos (360 + θ) = \cos θ t h u s, \cos (360 + 180) = \cos (540) \cos (180) = - 1$

Step 4. Calculation of tan(-405∘)

We know

$\tan (360 + 45) = \tan 45 A l s o \tan (- 45) = - \tan (45) t h e r e f o r e, \tan (- 405) = - 1$

Step 5. Final calculation

Substituting the values of trigonometric expression we get

$\cos 540 - \tan (- 405) = - 1 - (- 1) = - 1 + 1 = 0$

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Find the exact value of each expression. Do not use a calculator.
$\cos 540^{\circ} - \tan (- 405^{\circ})$

Short Answer

Step by step solution

Step 1. Given

Step 2. Concept

Step 3. Calculation of cos540∘

Step 4. Calculation of tan(-405∘)

Step 5. Final calculation

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Find the exact value of each expression. Do not use a calculator.cos540∘-tan(-405∘)

Short Answer

Step by step solution

Step 1. Given

Step 2. Concept

Step 3. Calculation of cos540∘

Step 4. Calculation of tan(-405∘)

Step 5. Final calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Mechanics Maths

Decision Maths

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find the exact value of each expression. Do not use a calculator.
$\cos 540^{\circ} - \tan (- 405^{\circ})$