Practice Trigonometry Questions and Answers

• 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 °
• If (sin 3A sec 6A = 1) , then what will be the value of cos 6A?
• If 17sin A = 8, where 0
• If √3cosec 2x = 2, then the value of x:
• In triangle ABC, ∠A - ∠B = 16 ° , whereas ∠A - ∠C = 8 ° , find ∠B.
• If cosx/siny = n and cosx/cosy = m, then the value of cos 2 y is: 1. m 2 /(m 2  + n 2 )2. 1/(m 2  + n 2 )3. n 2 /(m 2  + n 2 )4. 0...
• If sin(A + B) = sinAcosB + cosAsinB, then the value of sin75° is
• Calculate the value of sin120 o  + cos180 o  + tan225 o .
• cosx/(1 – sinx) + cosx/(1+ sinx) = 4, 0 o  < x < 90 o , then the value of (tanx + cosecx)
• What is the value of sin(B – C) cos(A – D) + sin(A – B) cos(C – D) + sin(C – A) cos(B – D)?
• If acos 3 θ + 3asin 2 θcosθ = m and asin 3 θ + 3asinθcos 2 θ = n, then find the value of (m + n) 2/3 + (m – n) 2/3 ....
• If 2ycosθ = x sinθ and 2xsecθ – ycosecθ = 3, then x 2 + 4y 2 = ?
• If tanθ – cotθ = a and cosθ + sinθ = b, then (b2 –1)(a2 + 4) = ?
• [(sinx – 2sin 3 x)/(2cos 3 x – cosx)] 2  + 1, x ≠45 o , is equal to:
• If secx – tanx = 1/√3, then the value of secx × tanx is:
• If cos θ + sin θ = m, sec θ + cosec θ = n then n(m 2 – 1) is equal to?
• ∆ PQR is right-angled at Q. If ∠R = 60º, then find the value of cosec P.
• Determine the value of following trigonometric expression: ...
• If sec 2P = sin² 60⁰ + sec 60⁰ - cos² 30⁰, then determine the value of (√3tan P + cot² P)
• If 2cosec 2  A – cot 2  A = 5 and 0 o  < A < 90 o , then find the value of ‘A’.
• Find the value of sin²50° + sin²40°.