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Maths Trigonometrical Ratios, Functions and Identities General Numeric Response

Published on: August 13, 2026

cos ( α – β ) = 1 and cos ( α + β ) = , where α , β ∈ [– π , π ]. Then number of ordered pairs ( α , β ) which satisfy both the equations.

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The correct answer is:

(4)

α – β = 0, – 2 π or 2 π

α – β = 0 ⇒ α = β ⇒ cos 2 β =

This is true for '4' value of ' α ', ' β '

If α – β = – 2 π ⇒α = – π and β = π

and cos ( α + β ) = 1 ⇒ (No solution)

similarly if α – β = 2 π⇒ α = π and β = − π again no solution results

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