Statement 1 - If I ( n ) = 2 cos n x , n ∈ N , then I ( 1 ) ⋅ I ( n + 1 ) − I ( n ) = I ( n + 3 ) . Statement 2 - cos C + cos D = 2 cos ( 2 C + D ) cos ( 2 C − D ) .

Question

Statement 1 - If I ( n ) = 2 cos n x , n ∈ N , then I ( 1 ) ⋅ I ( n + 1 ) − I ( n ) = I ( n + 3 ) . Statement 2 - cos C + cos D = 2 cos ( 2 C + D ​ ) cos ( 2 C − D ​ ) .

TestHub · Accepted Answer

I ( 1 ) I ( n + 1 ) − I ( n ) = 4 cos x cos ( n + 1 ) x − 2 cos n x = 2 { cos ( n + 2 ) x + cos n x } − 2 cos n x = 2 cos ( n + 2 ) x = I ( n + 2 ) , not I ( n + 3 ) . Statement 1 is false and Statement 2 is true.

Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

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