Set a , b ∈ [ − π , π ] such that cos ( a − b ) = 1 and cos ( a + b ) = e 1 . The number of pairs (a, b) satisfying the above system of equation is

Question

Set a , b ∈ [ − π , π ] such that cos ( a − b ) = 1 and cos ( a + b ) = e 1 ​ . The number of pairs (a, b) satisfying the above system of equation is

TestHub · Accepted Answer

∵ cos ( a − b ) = cos 0 ∴ a − b a − b ​ = 2 nπ , n ∈ Z = − 2 π , 0 , 2 π ​ ∴ ∴ ​ a + b = 2 π + 2 a , 2 a , 2 a − 2 π cos ( a + b ) = cos 2 a , cos 2 a , cos 2 a = e 1 ​ y = cos 2 a = e 1 ​ ​ Hence, number of solutions is 4.

Mathematics - Trigonometric Equation Question with Solution | TestHub

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JEE Advanced (2028)