# CAT Practice : Trigonometry

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Max and Min value of the given expression

## Trigonometric Identities

Q.13: If Cos x – Sin x = √2 Sin x, find the value of Cos x + Sin x:
1. √2 Cos x
2. √2 Cosec x
3. √2 Sec x
4. √2 Sin x Cos x

Choice A. √2 Cos x

## Detailed Solution

Cos x – Sin x = √2 Sin x

=) Cos x = Sin x + √2 Sin x

=) Cos x = Sin x + √2 Sin x

=) Sin x = $\frac{Cos x }{(√2 + 1)}$ * Cos x

=) Sin x = $\frac{(√2 - 1)}{(√2 - 1)} * \frac{1}{(√2 + 1)}$ * Cos x

=) Sin x = $\frac{(√2 - 1)}{((√2)^2- (1)^2)}$ * Cos x

=) Sin x = (√2 - 1) Cos x

=) Sin x = √2 Cos x – Cos x

=) Sin x + Cos x = √2 Cos x

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