Question
Download Solution PDFFind the general solution of the equation sin 2x + cos x = 0
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
General solutions of:
cos x = cos y ⇒ x = 2nπ ± y.
sin x = sin y ⇒ x = nπ + (-1)ny.
Calculation:
The given equation can be solved as:
sin 2x + cos x = 0.
⇒ 2 sin x cos x + cos x = 0
⇒ cos x (2 sin x + 1) = 0
⇒ cos x = 0 (or) (2 sin x + 1) = 0
i.e cos x = 0 (or) sinx = -1/2
⇒ cos x = cos π/2 OR sin x = sin (-π/6)
⇒ x = 2nπ +- π/2 OR x = nπ + (-1)n × (-π/6)
Additional Information General Solution of Trigonometric Functions
| Equations | Solutions |
| sin x = 0 | x = nπ |
| cos x = 0 | x = (2nπ +- π/2) |
| tan x = 0 | x = nπ |
| sin x = 1 | x = (2nπ + π/2) = (4n+1)π/2 |
| cos x = 1 | x = 2nπ |
| sin x = sin θ | x = nπ + (-1)nθ, where θ ∈ [-π/2, π/2] |
| cos x = cos θ | x = 2nπ ± θ, where θ ∈ (0, π] |
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