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.
30 questions
- Simplify the expression: \(\frac{\tan\theta-\sec\theta+1}{\tan\theta+\sec\theta-1}\).
- What is the value of \(\frac{2[\sin(21^\circ)\cos(69^\circ)+\cos(21^\circ)\sin(69^\circ)]+3\sec(54^\circ)\sin(36^\circ)}{\operatorname{cosec}^2(15^\circ)-\tan^2(75^\circ)}\)?
- If sin θ − cos θ = 3/5, find the value of sin θ + cos θ.
- If cosec θ − cot θ = √2 − 1, find the value of cosec θ + cot θ.
- Evaluate the value of the expression: 3(sin θ − cos θ)^4 + 6(sin θ + cos θ)^2 + 4(sin^6 θ + cos^6 θ).
- If cosec θ + cot θ = p, then find the value of \(\frac{p^2-1}{p^2+1}\).
- What is the value of \(\frac{\sin(18^\circ)\cos(72^\circ)+\sec(61^\circ)\sin(29^\circ)+\cos(18^\circ)\sin(72^\circ)+\operatorname{cosec}(61^\circ)\cos(29^\circ)}{\sec^2(48^\circ)-\cot^2(42^\circ)}\)?
- If 3 sin θ + 5 cos θ = 5, find the value of 5 sin θ − 3 cos θ.
- If \(\sec^2\theta+\tan^2\theta=\frac{7}{12}\), find the value of \(\sec^4\theta-\tan^4\theta\).
- If \(\sin\theta-\cos\theta=\frac45\), then find the value of \(\sin\theta+\cos\theta\).
- Simplify the expression: \((\sin\theta+\operatorname{cosec}\theta)^2+(\cos\theta+\sec\theta)^2-(\tan\theta+\cot\theta)^2\).
- Simplify: \((\sin A+\operatorname{cosec} A)^2+(\cos A+\sec A)^2-(\tan^2 A+\cot^2 A)\).
- In triangle ABC, AB=7 cm, BC=24 cm and AC=25 cm. Find the value of tan C + sin C + 2 cot A.
- If sec θ + tan θ = 5, where θ is an acute angle, find the value of sec θ.
- If sin(A + B) = sinAcosB + cosAsinB, then the value of sin 75° is:
- A man pulls a rope tied to a flagpole at ground level. The rope is 20 meters long and makes an angle of 60° with the ground. How high up…
- If x = 7sin A + 24cos A and y = 7cos A − 24sin A, then what is the value of 3(x² + y²)?
- If secx − tanx = 1/√3, then the value of secx × tanx is:
- 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: \(\frac{\cos(x)}{1+\sin(x)}+\frac{\sin(x)}{1+\cos(x)}\).