WBJEE · Maths · Trigonometric Equations
The equation \(\sin x(\sin x+\cos x)=k\) has real solutions, where k is a real number. Then,
- A \(0 \leq k \leq \frac{1+\sqrt{2}}{2}\)
- B \(2-\sqrt{3} \leq k \leq 2+\sqrt{3}\)
- C \(0 \leq k \leq 2-\sqrt{3}\)
- D \(\frac{1-\sqrt{2}}{2} \leq k \leq \frac{1+\sqrt{2}}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{1-\sqrt{2}}{2} \leq k \leq \frac{1+\sqrt{2}}{2}\)
Step-by-step Solution
Detailed explanation
Let, \(f(x)=\sin x(\sin x+\cos x)\) \(=\sin ^{2} x+\sin x \cos x\) \(=\frac{1-\cos 2 x}{2}+\frac{2 \sin x \cos x}{2}\) \(=\frac{1}{2}-\frac{1}{2} \cos 2 x+\frac{1}{2} \sin 2 x\) \(=\frac{1}{2}+\frac{1}{2}(\sin 2 x-\cos 2 x)\)…
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