Practice Trigonometric Identities Practice Questions with Detailed Solutions – Level 3

What is the product of the maximum and the minimum values of the expression \(8\sin \theta - 6\cos \theta + 5?\)

What is the value of \( \frac{\cos 38° \, \mathrm{cosec}\, 52°}{\tan 18° \tan 35° \tan 60° \tan 72° \tan 55°} \)?

What is the value of \( \frac{4}{3} \)cot²30° + 3sin²60° − 2cosec²60° − \( \frac{3}{4} \)tan²30°?

The expression \( \frac{\tan\theta + \sec\theta - 1}{\tan\theta - \sec\theta + 1} \) is equal to:

If \(x = a \sec\theta \cos\varphi\), \(y = b \sec\theta \sin\varphi\) and \(z = c \tan\theta\), then what is the value of \( \frac{x^2}{a^2} + \frac{y^2}{b^2} - \frac{z^2}{c^2} \)?

If \(\cos \theta + \cos^{2} \theta = 1,\) then what is the value of the following expression?

\(\sin^{12} \theta\) \({}+ 3\sin^{10} \theta\) \({}+ 3\sin^{8} \theta\) \({}+ \sin^{6} \theta\) \({}+ 2\sin^{4} \theta\) \({}+ 2\sin^{2} \theta\) \({}- 2\)

What is the maximum value of \(6\sin \theta\) \(\cos\theta + 4\cos 2\theta\)?

What is the value of the following expression?

(tan1° × tan2° × tan3° × … × tan89°) + (cos²1° + cos²2° + cos²3° + … + cos²89°)

If \(\tan\theta = p - \frac{1}{4p}\), where \(p > 0\) and \(\theta\) is acute, then \(\sec\theta + \tan\theta\) is equal to:

If \(\sec (2\theta + 10^{\circ})\) \({}= \operatorname{cosec} (4\theta - 40^{\circ}),\) where both angles are acute, what is the value of \(\sin^{2} (\theta + 10^{\circ})\) \({}+ \tan^{2} (2\theta + 5^{\circ})?\)