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If cosA + sinA = √2cosA, then prove that cosA - sinA = √2sinA
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If cosA + sinA = √2cosA, then prove that cosA - sinA = √2sinA
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If cosA + sinA = √2cosA, then prove that cosA - sinA = √2sinA
Given: cosA sinA = √2cosA
To Prove: cosA - sinA = √2sinA
Proof:
We can start by using the trigonometric identity: (cosA - sinA)^2 = cos^2 A + sin^2 A - 2sinAcosA.
Now, we need to manipulate the given equation to get it in a form that we can use to substitute into the identity above.
cosA sinA = √2cosA
Dividing both sides by cosA, we get:
sinA = √2
Now, substituting sinA = √2 into the equation, we get:
cosA √2 = √2cosA
Simplifying this, we get:
cosA = sinA
Now, we can substitute cosA = sinA into the identity above:
(cosA - sinA)^2 = cos^2 A + sin^2 A - 2sinAcosA
(sinA - sinA)^2 = sin^2 A + sin^2 A - 2sin^2 A
Simplifying this, we get:
0 = sin^2 A - sin^2 A
0 = 0
This is true, which means that our original equation is true. Therefore, we have proven that:
cosA - sinA = √2sinA
To Prove: cosA - sinA = √2sinA
Proof:
We can start by using the trigonometric identity: (cosA - sinA)^2 = cos^2 A + sin^2 A - 2sinAcosA.
Now, we need to manipulate the given equation to get it in a form that we can use to substitute into the identity above.
cosA sinA = √2cosA
Dividing both sides by cosA, we get:
sinA = √2
Now, substituting sinA = √2 into the equation, we get:
cosA √2 = √2cosA
Simplifying this, we get:
cosA = sinA
Now, we can substitute cosA = sinA into the identity above:
(cosA - sinA)^2 = cos^2 A + sin^2 A - 2sinAcosA
(sinA - sinA)^2 = sin^2 A + sin^2 A - 2sin^2 A
Simplifying this, we get:
0 = sin^2 A - sin^2 A
0 = 0
This is true, which means that our original equation is true. Therefore, we have proven that:
cosA - sinA = √2sinA
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If cosA + sinA = √2cosA, then prove that cosA - sinA = √2sinA
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If cosA + sinA = √2cosA, then prove that cosA - sinA = √2sinA for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If cosA + sinA = √2cosA, then prove that cosA - sinA = √2sinA covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cosA + sinA = √2cosA, then prove that cosA - sinA = √2sinA.
If cosA + sinA = √2cosA, then prove that cosA - sinA = √2sinA for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If cosA + sinA = √2cosA, then prove that cosA - sinA = √2sinA covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cosA + sinA = √2cosA, then prove that cosA - sinA = √2sinA.
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