Question

if cosø+sinø=√2 cosø show that cosø-sinø=√2 sinø

Answer 1

hi mate here is ur answer

the answer is correct so u can completely rely on it

so here u go with the answer

given to us is

cos ∅ - sin ∅ = √2 sin∅

cos ∅ = √2 sin∅ +sin∅

cos ∅ = sin ∅( √2 - 1)

multiplying both sides by the rationalizing factor of √2+1

that it √2 - 1

we get ,

cos ∅ (√2-1 ) = sin ∅ ( √2 + 1) (√2 - 1)

√2cos∅ - cos ∅ = sin ∅ (2-1)

√2 cos ∅ - cos ∅ = sin ∅

√2 cos ∅ = sin ∅ + cos ∅

hence proved

hope it helps !!!

mark as brainliest

Answer 2

Solution :

Here I am using angle A .

cosA + sinA = √2 cosA

Do the square both sides ,

( cosA + sinA )² = ( √2 cosA )²

=> cos²A+sin²A + 2cosAsinA = 2cos²A

=> sin²A+2cosAsinA=2cos²A -cos²A

=> sin²A = cos²A - 2cosAsinA

=>sin²A+sin²A =cos²A+sin²A-2cosAsinA

=> 2sin²A = ( cosA - sinA )²

=> √(2sin²A ) = √(cosA-sinA)²

=> √2 sinA = cosA - sinA

Therefore ,

cosA - sinA = √2 sinA

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