TS EAMCET · Maths · Trigonometric Ratios & Identities
If \(\cos x=\tan y, \cot y=\tan z\) and \(\cot z=\tan x\), then \(\sin x\) equals to
- A \(\frac{\sqrt{5}+1}{4}\)
- B \(\frac{\sqrt{5}-1}{4}\)
- C \(\frac{\sqrt{5}+1}{2}\)
- D \(\frac{\sqrt{5}-1}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{\sqrt{5}-1}{2}\)
Step-by-step Solution
Detailed explanation
Given, \(\cos x=\tan y, \cot y=\tan z\) and \(\cot z=\tan x\) \(\therefore \quad \cos x=\tan y\) \(\Rightarrow \quad \cos x=\frac{1}{\tan z}\) \(\Rightarrow \quad \cos x=\cot z\) \(\Rightarrow \quad \cos x=\tan x\) \(\Rightarrow \quad \cos x=\frac{\sin x}{\cos x}\)…
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