Practice Trigonometry Questions and Answers

• 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...
• 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?
• If x = (sin 30 ° + cos 30 ° )/sec 60 ° , then find the value of 4x.
• Find the simplified value of the following expression if a = 30o [(sin2a + cos2a} ÷ seca × sina ÷ cosa]...
• Calculate the value of sec75o
• If sinAo = (√3/2), then find the value of (sin245o + cos230o) × A ÷ 5 given that 0 < A < 90....
• Find the value of:  (Sin2 60 ° X cos 30 ° X sec 60°)/tan 30°
• What is the value of cos75°? 
• If 2cosθ + 8sin2θ = 11, where 0o < θ < 90o, then find the value of cot θ. 
• If {(tanx)/(secx)} × cosx = (1/2), then determine the value of ‘sin2x’.
• Find the simplified value of:
• If tan θ = (2/√5), then determine the value of cos2 θ
• If cosec (2A + B) = (2/√3) and cosec (A + B) = √2, then determine the value of (4A - B).
• Simplify the following trigonometric expression: 12 cos 68° cosec 22° - 3 cot 72° cot 18° ...
• 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 'θ' is an angle less than 120°, what is the value of 'θ' if it satisfies the equation 3cos2θ = 2 + sin2θ. ...
• If cosec2A = (sin60o + tan45o X sec245o), then find the value of sin2A.
• What is the value of (1 - sin A)/(1 + Sin A) given that tan A = 5/12 and 0° ≤ A ≤ 90°.
• If sin 2A = cos (3A - 60o) , then find the value of sec 2A.
• If 4cos2x - 3 = 0, and (0° > x > 90°), then find the value of 'x'.
• 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
• If sec2 θ = 4, then find the value of sin2 θ + cosec (90 - θ) where 0o < θ < 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}.