Chapter 7: Q. 1 (page 495)

$\cos (2 θ) = \cos^{2} θ -$ $=$ $- 1 = 1 -$ .

Short Answer

Expert verified

$\cos (2 θ) = {(\cos θ)}^{2} - \underset{⏝}{{(\sin θ)}^{2}} = \underset{⏝}{{2 (\cos θ)}^{2}} - 1 = 1 - \underset{⏝}{{2 (\sin θ)}^{2}}$ .

Step by step solution

Step 1. Given Data

The given incomplete equation is

$\cos (2 θ) = \cos^{2} θ -____=_____- 1 = 1 -______$

Step 2. Explanation

Use Sum formula of the cosine function

$\cos (θ + θ) = (\cos θ) (\cos θ) - (\sin θ) (\sin θ) \cos (2 θ) = {(\cos θ)}^{2} - {(\sin θ)}^{2} \cos (2 θ) = 1 - {(\sin θ)}^{2} - {(\sin θ)}^{2} \cos (2 θ) = 1 - {2 (\sin θ)}^{2}$

and

$\cos (2 θ) = {(\cos θ)}^{2} - (1 - {(\cos θ)}^{2}) \cos (2 θ) = 2 {(\cos θ)}^{2} - 1$

so $\cos (2 θ) = {(\cos θ)}^{2} - \underset{⏝}{{(\sin θ)}^{2}} = \underset{⏝}{{2 (\cos θ)}^{2}} - 1 = 1 - \underset{⏝}{{2 (\sin θ)}^{2}}$

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$\cos (2 θ) = \cos^{2} θ -$ $=$ $- 1 = 1 -$ .

Short Answer

Step by step solution

Step 1. Given Data

Step 2. Explanation

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cos2θ=cos2θ- = -1=1- .

Short Answer

Step by step solution

Step 1. Given Data

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Study anywhere. Anytime. Across all devices.

$\cos (2 θ) = \cos^{2} θ -$ $=$ $- 1 = 1 -$ .