Question
The value of k, for which
(cos x + sin x)2 + k sin x cos x - 1 = 0 is an identity, is
(cos x + sin x)2 + k sin x cos x - 1 = 0 is an identity, is
Answer: Option B
:
B
(b) Given,(cos x + sin x)2 + k sin x cos x - 1 = 0, ∀ x
⇒ cos2x +sin2x + 2cos x sin x + k sin x cos x - 1 = 0,∀ x
⇒ (k + 2)cos x sin x = 0,∀ x
⇒ k = -2
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:
B
(b) Given,(cos x + sin x)2 + k sin x cos x - 1 = 0, ∀ x
⇒ cos2x +sin2x + 2cos x sin x + k sin x cos x - 1 = 0,∀ x
⇒ (k + 2)cos x sin x = 0,∀ x
⇒ k = -2
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