Question

if cos theta -sin theta=√2 sin theta then cos theta + sin theta=?

Answer 1

Solution : (Instead of θ, I use A)

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Given :

Cos A - Sin A = √2 Sin A.....(1)

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To find:

The value of : Cos A + Sin A ,.

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We know that,

⇒ Cos A - Sin A = √2 Sin A

By squaring both the sides,

We get,.

⇒ (Cos A - Sin A)² = (√2 Sin A)²

⇒ Cos²A - 2 Cos A Sin A + Sin²A = 2 Sin² A

⇒ 1 - 2 Sin A Cos A = 2 Sin²A    (As,   Sin² A + Cos² A = 1)

⇒ - 2 Sin A Cos A = 2 Sin²A - 1

⇒  2 Sin A Cos A = 1 - 2 Sin²A

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By squaring the value to be found,

We get,.

⇒ Cos A + Sin A

⇒(Cos A + Sin A)²

⇒ Cos²A + 2 Sin A Cos A + Sin²A

⇒ 1 + 2 Sin A Cos A

⇒ 1 + 1 - 2 Sin² A

⇒  2 - 2 Sin²A

⇒ 2(Sin² A + Cos ²A) - 2 Sin²A

⇒  2 Cos² A

⇒ √2 Cos A  (That was squarred value,. So I took square root,.)

∴ Sin A + Cos A =  √2 Cos A

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                              Hope it Helps !!

⇒ Mark as Brainliest,.  (Sorry for Delay),.

Answer 2

Answer:

your answer attached in the photo