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Basic Trigonometric Identities

The value of ...

Question

The value of k, for which $(c o s x + s i n x)^{2} + k s i n x c o s x - 1 = 0$ is an identity, is

A

-1

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B

-2

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C

0

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D

1

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Solution

The correct option is B
-2

$G i v e n, (c o s x + s i n x)^{2} + k s i n x c o s x - 1 = 0, \forall x \Rightarrow c o s^{2} x + s i n^{2} x + 2 c o s x s i n x + k s i n x c o s x - 1 = 0, \forall x \Rightarrow (k + 2) c o s x s i n x = 0, \forall x \Rightarrow k + 2 = 0 \Rightarrow k = - 2$

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