A fairly straight forward method is the square both sides of the equation. However, in doing so, we will be introducing a potential "non solution" condition so we will need to đánh giá the answers we get lớn ensure they are all valid.

Bạn đang xem: Solving \$cos x+sin x

sin(x) − cos(x) = 1

(sin(x) − cos(x))2 = 12

sin2(x) - 2sin(x)cos(x) + cos2(x) = 1

sin2(x) + cos2(x) - 2sin(x)cos(x) = 1

Using the Pythagorean Identity sin2(x) + cos2(x) = 1:

1 - 2sin(x)cos(x) = 1

- 2sin(x)cos(x) = 0

sin(x)cos(x) = 0

So either sin(x) = 0 (meaning x = 0, π, và 2π) or cos(x) = 0 (meaning x = π/2 and 3π/2).

For x = 0: sin(0) - cos(0) = 1 is NOT true

For x = π: sin(π) - cos(π) = 1 is TRUE

For x = 2π: sin(2π) - cos(2π) = 1 is NOT true

For x = π/2: sin(π/2) - cos(π/2) = 1 is TRUE

For x = 3π/2: sin(3π/2) - cos(3π/2) = 1 is NOT true

So the answer turns out to lớn be x = π/2 và x = π

Upvote • 0 Downvote
địa chỉ cửa hàng comment
More
Report

## Still looking for help? Get the right answer, fast.

Get a miễn phí answer to lớn a quick problem. Most questions answered within 4 hours.

OR
Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.

¢ € £ ¥ ‰ µ · • § ¶ ß ‹ › « » > ≤ ≥ – — ¯ ‾ ¤ ¦ ¨ ¡ ¿ ˆ ˜ ° − ± ÷ ⁄ × ƒ ∫ ∑ ∞ √ ∼ ≅ ≈ ≠ ≡ ∈ ∉ ∋ ∏ ∧ ∨ ¬ ∩ ∪ ∂ ∀ ∃ ∅ ∇ ∗ ∝ ∠ ´ ¸ ª º † ‡ À Á Â Ã Ä Å Æ Ç È É Ê Ë Ì Í Î Ï Ð Ñ Ò Ó Ô Õ Ö Ø Œ Š Ù Ú Û Ü Ý Ÿ Þ à á â ã ä å æ ç trần é ê ë ì í î ï ð ñ ò ó ô õ ö ø œ š ù ú û ü ý þ ÿ Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ ς σ τ υ φ χ ψ ω ℵ ϖ ℜ ϒ ℘ ℑ ← ↑ → ↓ ↔ ↵ ⇐ ⇑ ⇒ ⇓ ⇔ ∴ ⊂ ⊃ ⊄ ⊆ ⊇ ⊕ ⊗ ⊥ ⋅ ⌈ ⌉ ⌊ ⌋ 〈 〉 ◊

### RELATED TOPICS

Math Algebra 2 Calculus Geometry Precalculus Algebra Word Problem Pre Calculus Maths Math Help ... Trig Trigonometry Identities Triangles Mathematics Math Word Problem Tangent Trigonometric Identities Trigonometric Functions Cosine Sine

### RELATED QUESTIONS

tan^2x-sin^2x=tan^2xsin^2x

I need help trying to sole tan^2 x =1 where x is more than or equal to lớn 0 but x is less than or equal to pi

find all solutions khổng lồ the equation in (0, 2pi) sin(6x)+sin(2x)=0

(2sin18)(cos18)

how vì i go about solving a trig identity; that simplify s 1-sin^2 theta/1-cos theta

### RECOMMENDED TUTORS Bill F.

5.0 (2,878) Abigail W.

5.0 (699) Abigail C.

5.0 (3,812)
See more tutors

### find an online tutor

tải về our free app

Xem thêm: Nhân Ngày 20-11 Kể Cho Các Bạn Nghe Về Một Kỉ Niệm Đáng Nhớ Giữa Mình Và Thầy Cô Giáo Cũ

Please provide a valid phone number.
Get lớn know us
Learn with us
Work with us
tải về our không tính tiền app
Let’s keep in cảm biến
Need more help?   