Practice Trigonometric Identities Practice Questions with Detailed Solutions – Level 2

If \(\sec \theta + \tan \theta = 4,\) then what is the value of \(\cos \theta?\)

What is the maximum value of \(8\sin \theta + 15\cos \theta + 3?\)

What is the value of \(\tan 10^{\circ} \cdot \tan 20^{\circ} \cdot \tan 30^{\circ} \cdot \tan 70^{\circ} \cdot \tan 80^{\circ}?\)

What is the value of \( \frac{\cos 37°}{\sin 53°} \) + sin²28° + sin²62° − tan15° · tan75°?

What is the value of \((\sin^{2} 30^{\circ} + 4\cot^{2} 45^{\circ} - \sec^{2} 60^{\circ})(\operatorname{cosec}^{2} 45^{\circ} \cdot \sec^{2} 30^{\circ})?\)

The expression \((1 + \tan^{2} \theta)(1 - \sin \theta)(1 + \sin \theta)\) simplifies to:

If \(\operatorname{cosec} \theta + \cot \theta = 5,\) then what is the value of \(\cos \theta?\)

If \(7\sin^{2} \theta + 3\cos^{2} \theta = 4,\) where \(\theta\) is an acute angle, then what is the value of \(\tan \theta?\)

What is the value of \((1 + \cot \theta - \operatorname{cosec} \theta)(1 + \tan \theta + \sec \theta)?\)

If \(\sin \theta + \cos \theta = \sqrt{2}\) \(\cos\theta\), then what is the value of \(\cot \theta?\)