AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(1+\sqrt{1+a}=(1+\sqrt{1-a}) \cot \alpha\) and \(0 < a < 1\), then \(\sin 4 \alpha=\)
- A a
- B \(2 a\)
- C \(3 \mathrm{a}\)
- D \(4 a\)
Answer & Solution
Correct Answer
(A) a
Step-by-step Solution
Detailed explanation
Given \((1+\sqrt{1+a})=(1+\sqrt{1-a}) \cot \alpha\) \[ \begin{aligned} & \Rightarrow \quad(1+\sqrt{1+a}) \sin \alpha=(1+\sqrt{1-a}) \cos \alpha \\ & \Rightarrow \quad(\sin \alpha-\cos \alpha)=(\sqrt{1-a} \cos \alpha-\sqrt{1+a} \sin \alpha) \end{aligned} \] Squaring both side we…
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