Practice Trigonometric Identities Practice Questions with Detailed Solutions – Level 1

If \(\sin \theta = \dfrac{3}{5}\) and \(\theta\) is an acute angle, what is the value of \(\cos \theta?\)

What is the value of 5sec²θ − 5tan²θ + 2?

If \(\operatorname{cosec} \theta - \cot \theta = \dfrac{1}{3},\) what is the value of \(\operatorname{cosec} \theta + \cot \theta?\)

What is the value of \( \frac{\sin 35°}{\cos 55°} \) + \( \frac{\tan 20°}{\cot 70°} \)?

What is the value of \(\sin^{2} 30^{\circ}\) \({}+ \cos^{2} 60^{\circ}\) \({}+ \tan^{2} 45^{\circ}?\)

The expression \((1 - \cos^{2} \theta)(1 + \cot^{2} \theta)\) is equal to:

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

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

What is the maximum value of \(3\sin \theta + 4\cos \theta?\)

What is the minimum value of \(6\sin \theta + 8\cos \theta?\)