Which one of the following is true? (a) tan (x) > 1 ; 45° 1 2 ; 0° 1 2 ; 60° < (x) < 90° (d) sin (x) = cos (x) for some value of (x); 30° < (x) < 45°

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1.	Which one of the following is true? (a) tan \(x\) > 1 ; 45° < \(x\) < 90° (b) sin \(x\) > 1 2 ; 0° < \(x\) < 30° (c) cos \(x\) > 1 2 ; 60° < \(x\) < 90° (d) sin \(x\) = cos \(x\) for some value of \(x\); 30° < \(x\) < 45°
Answer» (a) tan \(x\) > 1 ; 45° < \(x\) < 90° tan 45° = 1 and tan 90° = undefined (∞) ∴ when \(x\) lies between 45° and 90°, tan \(x\) > 1.

Which one of the following is true? (a) tan \(x\) > 1 ; 45° < \(x\) < 90° (b) sin \(x\) > 1 2 ; 0° < \(x\) < 30° (c) cos \(x\) > 1 2 ; 60° < \(x\) < 90° (d) sin \(x\) = cos \(x\) for some value of \(x\); 30° < \(x\) < 45°

Answer»

(a) tan \(x\) > 1 ; 45° < \(x\) < 90°

tan 45° = 1 and tan 90° = undefined (∞)

∴ when \(x\) lies between 45° and 90°, tan \(x\) > 1.

Discussion

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Which one of the following is true? (a) tan \(x\) &gt; 1 ; 45° &lt; \(x\) &lt; 90° (b) sin \(x\) &gt; 1 2 ; 0° &lt; \(x\) &lt; 30° (c) cos \(x\) &gt; 1 2 ; 60° &lt; \(x\) &lt; 90° (d) sin \(x\) = cos \(x\) for some value of \(x\); 30° &lt; \(x\) &lt; 45°

Which one of the following is true? (a) tan \(x\) > 1 ; 45° < \(x\) < 90° (b) sin \(x\) > 1 2 ; 0° < \(x\) < 30° (c) cos \(x\) > 1 2 ; 60° < \(x\) < 90° (d) sin \(x\) = cos \(x\) for some value of \(x\); 30° < \(x\) < 45°