AP EAMCET · Maths · Trigonometric Ratios & Identities
The equation \(\sin ^4 x+\cos ^4 x=a\) has real solutions, then
- A \(1 < a < \frac{5}{2}\)
- B \(\frac{1}{2} \leq a \leq 1\)
- C \(a \leq \frac{1}{2}\)
- D \(0 < \) a \( < 1\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2} \leq a \leq 1\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \sin ^4 x+\cos ^4 x=\alpha \text { has real solution. } \\ & \text { Since, } \begin{aligned} & \alpha=\sin ^4 x+\cos ^4 x \\ &=\left(\sin ^2 x+\cos ^2 x\right)^2-2 \sin ^2 x \cdot \cos ^2 x \\ &=(1)^2-\frac{4}{2} \sin ^2 x \cos ^2 x=1-\frac{(2 \sin x…
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