Practice Trigonometry Questions and Answers

• If θ is an acute angle and sin θ + cosec θ = 2, then the value of sin2 θ + cosec2 θ is:
• If tan A = 4/3, 0 ≤ A ≤ 90°, then find the value of sec A.
• which of the following is equal to [(tan θ +secθ -1)/ (tanθ-secθ +1)]  
• Simplify (cos13°+sin 13°) /(cos13°-sin13°)
• Simplify (cos20°+sin 20°) /(cos20°-sin20°)
• If (sinx + siny) = a and (cosx + cosy) = b, then find the value of (sinx siny + cosx cosy). [A] (a²+b²-2)/ 2 [B] (a2-b2-2)/ 2 [C] (a²+b²-1)/ 2 [D](a²+...
• If sin x + cos x = √2 sin x, then the value of sin x - cos x is:
• If cos² x + sin x = 5/4, then find the value of 'sin x'.
• Simplify: sin 780° sin 480° + cos 120° sin 30°
• If x = r sin A cos B, y = r sin A sin B and z = r cos A, then find x² + y² + z².
• Find the value of sin 30°.
• If tan α = 1/2, tan β = 1/3, then find α + β.
• Simplify: sin (A + B) sin (A - B)
• If √3cosec 2x = 2, then the value of x:
• Find the value of sin265o + sin225o + cos235o + cos255o....
• If sin(3θ) = cos(2θ), then find the value of θ between 0 and 90 degrees.
• Find the value of tan(75°) using the identity for tan(A+B).
• Find the value of sin(θ) if 2sinθ = tanθ, for 0 < θ < 90°.
• If cos(2θ) = 1 - 2sin²(θ) and tan(θ) + cot(θ) = k, find the value of k when sin(θ) = 3/5.
• Solve for x in the interval [0, 2π]: 2 sin²x + 3 sinx - 2 = 0.
• If tan θ + cot θ = 5, find the value of tan²θ + cot²θ.
• If sec²x + csc²x = 10, find the value of tan²x + cot²x.
• A tower is 60 meters high. From a point on the ground, the angle of elevation of the top of the tower is 30°. Find the distance of the point from the base...
• A man is standing at a point 40 meters away from a tower. The angle of elevation of the top of the tower from the point is 45°. After walking 20 meters to...
• If sin(x + y) = 3/5 and cos(x - y) = 12/13, where x, y ∈ [0, π/2], find sin(2x) + sin(2y).
• A ladder leans against a wall. The foot of the ladder is 6 meters away from the wall. If the angle the ladder makes with the ground is 60°, find the lengt...
• From the top of a building, the angle of depression of two cars on a straight road are 30° and 60° respectively. If the height of the building is 120 met...
• What is the value of 4/3 (sin ² 65 º + sin ² 25 º ).
• If sin(x + y) = 1 and sin(x - y) = (1/2), then what is the value of sinx cosx + 2sin2y + cos2y? 
• If sin A = 3/5 and cos B = 4/5, where A and B are acute angles, find the value of sin(A + B).
• The angles of elevation of the top of a flagpole from two points A and B on level ground are 30° and 60° respectively. The points A and B are on the same...
• A point P is 15 meters away from the base of a building. The angle of elevation to the top of the building is 60°, while the angle of elevation to the top...
• A ladder is leaning against a wall, making an angle of 60° with the ground. The top of the ladder reaches a window 15 meters above the ground. Find the le...
• If tan θ = 4/3 and θ is an acute angle, find the value of sin θ + cos θ.
•  If sin θ = 3/5 and cos θ = 4/5, find the value of (2tan² θ + 3cot² θ).
• From a point 50 meters away from the base of a tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower.
• A man is standing at a point 20 meters away from a vertical tower. The angle of elevation from the point to the top of the tower is 60°. Find the height o...
• From a point on the ground, the angle of elevation of the top of a building is 45°. After walking 10 meters towards the building, the angle of elevation i...