Question

Which one of the following is possible ?

• A. $\cos \theta = \frac {7}{3} $
• B. $\sin \theta = \frac {a^2+b^2}{a^2-b^2} (a \neq b)$
• C. $\sec \theta =\frac {4}{5}$
• D. $\tan \theta =45$

Answer 1

Answer: (D)

(a) Suppose $a=2, \,\,\,\,\,\,\,b=1$
$\sin \,\theta=\frac{2^{2}+1^{2}}{2^{2}-1}=\frac{5}{3}>1$, 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.