AP EAMCET · Maths · Inverse Trigonometric Functions
If \(\theta\) is an acute angle, \(\cos h x=K\) and \(\sin h x=\tan \theta\), then \(\sin \theta=\)
- A \(\frac{K}{K^2+1}\)
- B \(\frac{K^2+1}{K^2+2}\)
- C \(\frac{\sqrt{K^2-1}}{K}\)
- D \(\frac{\sqrt{K^2-1}}{\sqrt{K^2+1}}\)
Answer & Solution
Correct Answer
(C) \(\frac{\sqrt{K^2-1}}{K}\)
Step-by-step Solution
Detailed explanation
\(\cosh x=K\) Since, \(\cos h ^2 x+\sin h^2 x=1\) \(\Rightarrow \sinh x=\sqrt{K^2-1} \Rightarrow \tan \theta=\frac{\sqrt{K^2-1}}{1}=\frac{P}{B}\) Let \(\mathrm{P}=\lambda \sqrt{K^2-1}, \mathrm{~B}=\lambda \Rightarrow \mathrm{H}=\lambda K\)…
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