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The question is from CAT Geometry - Trigonometry. This is about Trigonometric Identities. We need to find out value of a trigonometric function. Trigonometry is an important topic for CAT Preparation for the CAT Exam. Trigonometric ideas can be completely opposite, as in, some questions test lot of common sense with direction, heights and distances, while others could test you on identities. CAT exam could test one on both these fronts. Make sure you master both in CAT - Trigonometry.

Question 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

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Method of solving this CAT Question from CAT Geometry - Trigonometry : How you would relate the given and the asked term?

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

The question is "To find the value of Cos x + Sin x"

Hence, the answer is √2 Cos x

Choice A is the correct answer.

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