Consider the following statements:<br>1. The value of \cos 61^\circ + \sin 29^\circ <strong>CANNOT</strong> exceed 1.<br>2. The value of \tan 23^\circ - \cot 67^\circ is less than 0.<br>Which of the above statements is/are correct?

Explanation

Stmt 1: \cos 61^\circ = \sin(90^\circ-61^\circ) = \sin 29^\circ. So, \cos 61^\circ + \sin 29^\circ = 2\sin 29^\circ. Since \sin 30^\circ = 0.5, \sin 29^\circ \lt 0.5, which means 2\sin 29^\circ \lt 1. So it cannot exceed 1 (True). Stmt 2: \cot 67^\circ = \tan(90^\circ-67^\circ) = \tan 23^\circ. So, \tan 23^\circ - \cot 67^\circ = 0. Since it is exactly 0, it is not strictly less than 0 (False).

Related questions on Trigonometry

• Two poles are situated 24 m apart and their heights differ by 10 m. What is the distance between their tips?
• If \frac{\cos \theta}{1 - \sin \theta} + \frac{\cos \theta}{1 + \sin \theta} = 4, then which one of the following is a value of $(\tan^2 \...
• For 0 < \theta < \frac{\pi}{2}, consider the following : I. $(\tan^4 \theta + \tan^6 \theta)(\cot^4 \theta + \cot^6 \theta) = \sec^2 \the...
• If 3\sin \theta + 4\cos \theta = 5, then what is a value of 4\tan \theta + 3\cot \theta ?
• At a point on level ground, the tangent of the angle of elevation of the top of a tower is found to be \frac{5}{6}. On walking 70 m toward...