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Answer» Definition:An equation involving one or more trigonometrical ratio of an unknown angle is called a trigonometrical equationA trigonometric equation is different from a trigonometrical identities. An identity is satisfied for every value of the unknown angle\xa0e.g., cos2\xa0x = 1 − sin2\xa0x is true ∀ x ∈ R, while a trigonometric equation is satisfied for some particular values of the unknown angle.(1) Roots of trigonometrical equation:\xa0The value of unknown angle (a variable quantity) which satisfies the given equation is called the root of an equation,\xa0e.g., cos θ = ½, the root is θ = 60° or θ = 300° because the equation is satisfied if we put θ = 60° or θ = 300°.(2) Solution of trigonometrical equations:\xa0A value of the unknown angle which satisfies the trigonometrical equation is called its solution.Since all trigonometrical ratios are periodic in nature, generally a trigonometrical equation has more than one solution or an infinite number of solutions. There are basically three types of solutions:\tParticular solution:\xa0A specific value of unknown angle satisfying the equation.\tPrincipal solution:\xa0Smallest numerical value of the unknown angle satisfying the equation (Numerically smallest particular solution).\tGeneral solution:\xa0Complete set of values of the unknown angle satisfying the equation. It contains all particular solutions as well as principal solutions.Trigonometrical equations with their general solution\tTrigonometrical equationGeneral solutionsin θ = 0θ = nπcos θ = 0θ = nπ + π/2tan θ = 0θ = nπsin θ = 1θ = 2nπ + π/2cos θ = 1θ = 2nπsin θ = sin αθ = nπ + (−1)nαcos θ = cos αθ = 2nπ ± αtan θ = tan αθ = nπ ± αsin2\xa0θ = sin2\xa0αθ = nπ ± αtan2\xa0θ = tan2\xa0αθ = nπ ± αcos2\xa0θ = cos2\xa0αθ = nπ ± αsin θ = sin α cos θ = cos αθ = nπ + αsin θ = sin α tan θ = tan αθ = nπ + αtan θ = tan α cos θ = cos αθ = nπ + α\tGeneral solution of the form a cos θ + b sin θ = c\xa0
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