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Chapter - TRIGONOMETRY Std- 10 sub- mathematics QUESTION: if cos(x) + sin(x) = sqrt2...

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mun55 | Student, Grade 10 | eNoter

Posted June 16, 2012 at 1:12 PM via web

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Chapter - TRIGONOMETRY Std- 10 sub- mathematics QUESTION: if cos(x) + sin(x) = sqrt2 cos(x) , then prove that cos(x) - sin(x) = sqrt2 sin(x)

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted June 16, 2012 at 1:45 PM (Answer #1)

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You need to write sin x in terms of cos x, using the condition provided by the problem, such that:

`sin x = sqrt2*cos x - cos x`

You need to substitute `sqrt2*cos x - cos x`  for sin x in the identity to be proved such that:

`cos x - (sqrt2*cos x - cos x) = sqrt2 sin x`

You need to open the brackets such that:

`cos x - sqrt2*cos x + cos x = sqrt2*sin x`

`cos x - sqrt2*cos x = sqrt2*sin x`

You need to factor out cos x such that:

`cos x(1 - sqrt2) = sqrt2*sin x` 

Notice that the left side is not equal to the right side, hence, the expression `cos(x) - sin(x) = sqrt2 sin(x)`  is not an identity.

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