Practice Trigonometry Questions and Answers

• 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...
• 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.
• 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?
• Calculate the value of sec75o
• Find the value of:  (Sin2 60 ° X cos 30 ° X sec 60°)/tan 30°
• Find the simplified value of:
• If tan θ = (2/√5), then determine the value of cos2 θ
• Determined the simplified value of the given expression:(1 - sin2 q) X (sec q + tan q) X (sec q - tan q) X cosec2 q
• If 3 tan X + cot X = 2√3, then find the value of 6 tan2 X + 2 cot2 X.
• If sin (2x + 50) o = cos (2y - 50) o, such that, 0o < x + y < 90o, then find the value of tan(x + y) .
• If then find the value of 'b'...
• If sec(2A + B) = 2 and cos(A + B) = (1/√2) , find the value of {sec 2B + tan (A + B) } given that 0o < A, B < 90o
• Simplify the given equation:
• If tan 4θ = cot 14θ, then find the value of cos 9θ.
• If cos2B = sin(1.5B - 36 o ) , then find the measure of 'B'.
• Find the simplified value of the expression:sin 2 45 o  + sin 2 60 o  - (1/3) X tan 2 60 o  - cos 2 60 o...
• If cosec [180° − (3q/2) ] = √2, 0° < q < 90°, then find the value of {(2/√3) X cos q - 4 cos 3q}.
• If cos θ = (4x² – 1)/(1 + 4x²) then find the value of sin q.
• Determine the value of:(sin 38 o cos 52 o  + cos 2  38 o ) X sin 30 o  + (cos 60 o tan 45 o ) X sec 60 o ...
• If sec 4A = cosec (3A - 50°), where 4A and 3A are acute angles, find the value of A + 75.
• If 5tanθ = 12, then find the value of (sinθ – cosθ).
• If sin (a + b) = (√3/2) and cos (a – b) = (√3/2), then find sin a.
• sin1440° - cot630° - sin120°cos150° is equal to:
• In a triangle ABC, if 5∠A = 3∠B = 15∠C, then find the value of cosA + sin(C + 10 ° )
• If tan3θ = 1, then find the value of: (sin² 2θ/sec 3θ + 15°)
• A 16-meter-long rope is stretched from the ground to the top of a house, forming a 30° angle with the ground. Determine the height of the house.
• In a triangle ABC, if 5∠A = 3∠B = 15∠C, then find the value of cosA + sin(C + 25 ° )
• Calculate the maximum and minimum value of (8cosA + 15sinA + 15), if 'q' lies in the first quadrant.
• If 2cosA + secA = 2√2 , 0° < < 90°, then the value of 2(sec 4 A + cosec 4 A) is:
• If sec 2A = sin2  60o  + sec 60o  - cos2 30 o , then find the value of (√3tan A + cot 2  A)....
• Find the value of sin 240 °