Question

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Answer 1

$Question:$

Given:

If Cos∅ + Sin∅ = √2 Cos∅

To prove :

Cos∅ - Sin∅ = √2 Sin∅

Here,

Cos ∅ + Sin ∅ = √2 Cos∅

⇒ Sin∅ = √2 Cos∅ - Cos∅

⇒ Sin∅ = Cos∅ ( √2 -1 )

Multiplying by (√2+1) both side , we get

⇒ Sin∅ ( √2+1 ) =  Cos∅ (√2-1 ) (√2+1 )

[a² - b² = (a+b)(a-b)]

⇒ √2 Sin∅ + Sin∅ = Cos∅

∴ Cos∅ - Sin∅ = √2 Sin∅.

Hence proved.

Thanks.