Trigonometry
Trigonometry
Allen Star Batch
Grade 11

Question:

Which of the following is/are true?
$\tan 1>\tan^{-1}1$
$\sin 1>\cos 1$
$\tan 1\frac{1}{\sqrt{2}}$

Step-by-Step Solution

Key Concept: Tangent addition formulas and complementary angle relationships create polynomial equations connecting angles in arithmetic progression.
For option (A), $\tan l > \tan^{-1}$ implies $\tan l > \frac{\pi}{4}$. For option (B), comparing $\sin 57.3° > \cos 57.3°$ works since $57.3° > 45°$. Option (C) is impossible because $\tan 57.3° > 1$ while $\sin 57.3° \cos(\frac{\pi}{4})$ by the decreasing nature of cosine on $[0,\pi]$.
Correct Answer: 1,2,4

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