Question

if 13a =π then show that cos3a+ cos 5a+2cosa.cos9a=0

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Given :--

1. 13a = π

Formulas used :--

1. Cos c + Cos d = 2. [ Cos {(c+d)/2} . Cos {(c-d)/2}]

2. Cos (π/2) = Cos (180°/2) = Cos 90° = 0

Cos 3a + Cos 5a + 2. Cos a . Cos 9a

=(2. Cos {(5a + 3a )/2}. Cos {(5a- 3a)/2} ) +2. Cos a. Cos 9a

= 2. Cos 4a . Cos a + 2. Cos a . Cos 9a

= 2. Cos a ( Cos 4a + Cos 9a )

= 2. Cos a . { 2. Cos (13a/2) . Cos (5a/2)}

= 2. Cos a . { 2. Cos (π/2) . Cos (5a/2)}

= 2. Cos a . { 2. Cos 90° . Cos (5a/2)}

= 2. Cos a. {2. 0 . Cos (5a/2)}

= 0

LHS = RHS =0 【 hence proved】