Question

Cos theta - sin theta = root 2 sin theta then prove cos theta + sin theta = root cos theta

Answer 1

$\large\underline\mathfrak{\sf{\red{Question-}}}$

If CosØ - SinØ = √2SinØ, then prove that CosØ + SinØ = √2CosØ

$\large\underline\mathfrak{\sf{\red{Explanation-}}}$

CosØ - SinØ = √2SinØ ( Given )

Squaring both sides,

(CosØ - SinØ)² = (√2SinØ)²

★ ( CosØ - SinØ )² = Cos²Ø + Sin²Ø - 2CosØSinØ

$\implies$ Cos²Ø + Sin²Ø - 2CosØSinØ = 2Sin²Ø

$\implies$ Cos²Ø - 2CosØSinØ = 2Sin²Ø - Sin²Ø

$\implies$ Cos²Ø - 2CosØSinØ = Sin²Ø

$\implies$ Sin²Ø + 2CosØSinØ = Cos²Ø

Adding Cos²Ø both sides,

$\implies$ Sin²Ø + 2CosØSinØ + Cos²Ø = Cos²Ø + Cos²Ø

★ ( SinØ + CosØ )² = Sin²Ø + 2CosØSinØ + Cos²Ø

$\implies$ ( SinØ + CosØ )² = 2Cos²Ø

$\implies$ SinØ + CosØ = √(2Cos²Ø)

$\implies$ SinØ + CosØ = √2CosØ

Hence proved!

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Answer 2

Answer:

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