Trigonometry Questions
Trigonometry explores the relationships between angles and sides of triangles. Practise sine, cosine, tangent, and standard trigonometric formulas with step-by-step solutions designed for competitive examinations.
12 questions
- If 2 × sin q × cos(90° − q) = 1/2, where 0° < q < 90°, then find the value of sin(2q) + cos(2q).
- Find the value of (tan 20°)²/(cosec 70°)² + (cot 20°)²/(sec 70°)² + 2 tan 15° tan 45° tan 75°.
- If \(\cos A=\frac{12}{13}\), find the values of \(\sin A\) and \(\cot A\).
- If \(\tan(\theta)=\frac{12}{5}\) in a right-angled triangle, what is the length of the hypotenuse?
- Simplify: \(\frac{1+\sin(x)}{1-\cos(x)}+\frac{1-\sin(x)}{1+\cos(x)}\)
- If \(\sin A=\frac{3}{5}\) and \(\cos B=\frac{5}{13}\), find \(\sin A\cos B+\cos A\sin B\).
- Simplify: \(\frac{\cos(x)}{1+\sin(x)}+\frac{\sin(x)}{1+\cos(x)}\).
- Simplify the expression: \(\sin x\cot x+\cos x\tan x\).
- In a right triangle ABC, right-angled at B, if \(\tan A=1\), what is the value of \(2\sin A\cos A\)?
- If \(\sin\theta=\frac7{25}\), find \(\cos^2\theta\).
- Simplify: \(\frac{1+\tan^2(x)}{1+\cot^2(x)}\times\frac{\sec(x)-\tan(x)}{\sec(x)+\tan(x)}\)
- If \(\cos A=\frac{12}{13}\) and \(\sin B=\frac{5}{13}\), find \(\sin A\cos B+\cos A\sin B\).