KCET · Maths · Trigonometric Ratios & Identities
Which one of the following is possible?
- A \(\sin \theta=\frac{a^{2}+b^{2}}{a^{2}-b^{2}},(a \neq b)\)
- B \(\sec \theta=\frac{4}{5}\)
- C \(\tan \theta=45\)
- D \(\cos \theta=\frac{7}{3}\)
Answer & Solution
Correct Answer
(C) \(\tan \theta=45\)
Step-by-step Solution
Detailed explanation
(a) Suppose \(a=2, \quad b=1\)
\(\sin \theta=\frac{2^{2}+1^{2}}{2^{2}-1}=\frac{5}{3}>1\), which is not possible.
(b) \(\sec \theta=\frac{4}{5} < 1\), which is not possible.
(c) \(\tan \theta=45\), which is possible.
(d) \(\cos \theta=\frac{7}{3}>1\), which is not possible.
Hence, option (c) is correct.
\(\sin \theta=\frac{2^{2}+1^{2}}{2^{2}-1}=\frac{5}{3}>1\), which is not possible.
(b) \(\sec \theta=\frac{4}{5} < 1\), which is not possible.
(c) \(\tan \theta=45\), which is possible.
(d) \(\cos \theta=\frac{7}{3}>1\), which is not possible.
Hence, option (c) is correct.
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