Practice Trigonometry Questions and Answers

• 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...
• A person is standing at a point 120 meters away from a tower. The angle of elevation to the top of the tower is 60°. If the height of the tower increases ...
• A man observes the top of a tower at an angle of elevation of 30°. He walks 100 meters closer to the tower, and the angle of elevation becomes 60°. If th...
• A flagpole stands on top of a building. From a point 50 meters away from the base of the building, the angle of elevation to the top of the building is 30�...
• Find the simplified value of: (tan 40 º  +  tan 20 º )/(1 -  tan 40 º  tan 20 º)
• If tanθ = (2/√5), then find the value of cos2 θ
• Two buildings are 40 meters apart. The height of one building is 20 meters. From the top of the shorter building, the angle of elevation of the top of the ...
• In a right triangle ABC, angle B = 90°. If tan A = 3/4 and the length of the hypotenuse is 25 cm, find the area of the triangle.
• If sin θ + cos θ = 1.2, find the value of sin θ. cos θ.
• Find the value of (cos 60 º + sin 60 º) /(tan 60 º + cot 45 º) .
• The value of (sin 60 º cos 30 º - cos 60 º sin 30 º)  is equal to:
• If sin(3x - 2o) = cos(2x + 22o), then find the value of: {3tan(4x - 11o) + cosec(5x - 10o)} X cot(2x + 2o)...
• Find the value of (1 - sin2q) X (secq + tanq) X (secq - tanq) X cosec2q
• If tan 4θ = cot 14θ, then find the value of cos 9θ.
• ...
• If (sin 3A sec 6A = 1) , then what will be the value of cos 6A?
• If x = (sin 30 ° + cos 30 ° )/sec 60 ° , then find the value of 4x.