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Chapter - TRIGONOMETRY Std- 10 sub- mathematics QUESTION: if cos(x) + sin(x) = sqrt2...
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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.
Posted by sciencesolve on June 16, 2012 at 1:45 PM (Answer #1)
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