Introduction to Trigonometry Important Questions Prove that: (1 + cot² θ) (1 – cos θ) (1 + cos θ) = 1 Read More » Prove that (1 + cot^2 A) / (1 + tan^2 A) = cot^2 A Read More » Prove that 1 + tan^2 A = sec^2 A Read More » If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q (p2 – 1) = 2p Read More » Evaluate: (5 cos 2 60 + 4 sec 2 30 – tan 2 45) / (sin 2 30 + sin 2 60) Read More » If sin (A – B) = 1/2, cos (A + B) = 1/2; 0 < A + B <= 90°, A > B; find ∠ A and ∠ B. Read More » Prove that : (sin θ – cos θ + 1) / (sin θ + cos θ – 1) = 1/ (sec θ – tan θ) Read More » Evaluate : 5 tan 60° / (sin2 60° + cos2 60°) tan 30° Read More » In Δ ABC, if AD ⊥ BC and AD2 = BD x DC, then prove that ∠BAC = 90° Read More » Prove that : (cosec θ – sin θ) (sec θ – cos θ) (tan θ + cot θ) = 1 Read More » Evaluate : (sec2 45° – tan2 45°)/sin2 45° Read More » Prove that (sin A + cos A)/(sin A – cos A) + (sin A – cos A)/(sin A + cos A) = 2/(2 sin2 A – 1) Read More » Evaluate: (2𝑠𝑖𝑛 2 60 − 𝑡𝑎𝑛 2 30) / 𝑠𝑒𝑐2 45 Read More » If cosθ + sinθ = 1 , then prove that cosθ – sinθ = ±1 Read More » Evaluate : (cos 45° + sin 60°) / (sec 30° + cosec 30°). Read More » Prove that (sin θ – 2 sin3 θ) / (2 cos3 θ – cos θ) = tan θ Read More » Prove that (cosec 2 θ – sec 2 θ) / (cosec 2 θ + sec 2 θ) = 3/4, if tan θ = 1/√7. Read More » prove that sin 6 θ + cos 6 θ = 1 – 3 sin 2 θ cos 2 θ Read More » If 2sin(A + B) = √3 and cos(A – B) = 1 , then find the measures of angles A and B. 0 <= A B, (A + B) <= 90 deg Read More » Evaluate: 2 sin 2 30 sec 60 + tan 2 60 Read More » Prove that : 1 + sec θ – tan θ / 1 + sec θ + tan θ = 1 – sin θ / cos θ Read More » Evaluate: cos 45 / (sec 30 + cosec 30) Read More » Prove that Root ( sec^2 θ + csc^2 θ) = tan θ + cot θ Read More » If x sin^3 θ + y cos^3 θ = sin θ cos θ and x sin θ = y cos θ, prove that x^2 + y^2 = 1 Read More » Evaluate: 2√2 cos 45° sin 30° + 2√3 cos 30° Read More » If A = 60° and B = 30°, verify that : sin (A + B) = sin A cos B + cos A sin B Read More » Prove that : tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + sec θ cosec θ Read More » If sin A = 3/5 and cos B = 12/13 , then find the value of (tan A + tan B) Read More » If tan θ + sec θ = m, then prove that sec θ = (m2 + 1)/2m Read More » Prove that : tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + tan θ + cot θ Read More » If x = a sec(theta) + b tan theta and y = a tan theta + b sec(theta), prove that x ^ 2 – y ^ 2 = a ^ 2 – b ^ 2 Read More » If sec α = 2/√3, then find the value of 1- cosec α /1+ cosec α , where α is in IV quadrant. Read More » If cotθ = 15/8, then evaluate (2 + 2 sinθ)(1 – sinθ)/(1 + cosθ)(2 – 2 cosθ) Read More » IF Sec θ=(x+1/4x) then prove that secθ +tanθ =2x or 1/2x Read More » If sec θ + tan θ = p, obtain the values of sec θ, tan θ and sin θ in terms of p. Read More » If sin θ = 3/4, prove that Root [(cosec 2θ − cot 2 θ} / (sec 2 θ − 1)] = √7 / 3 Read More » If cosec2θ (1 + cosθ)(1 – cosθ) = λ, then find the value of λ. Read More » Prove that tan A / (1+ sec A) – tan A / (1- sec A) = 2 cosec A Read More » If 1 + sin^2 θ = 3 sin θ cos θ, then prove that tan θ = 1 or 1/2 Read More » Find the value of x if 2 cosec2 30 + x sin2 60 – 3/4 tan2 30 = 10 Read More » If tan (A + B) = √3 and tan (A – B) = 1/(√3) ; 0° < A + B < 90°; A > B, find A and B. Read More » Prove that: tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + sec θ cosecθ Read More » Prove that root[(sec A – 1)/(sec A + 1)] + root[(sec A + 1)/(sec A – 1)] = 2 cosec A Read More » If a cos θ + b sin θ = m and a sin θ – b cos θ = n, then prove that a2 + b2 = m2 + n2 Read More » If sin θ – cos θ = 0, then find the value of sin^4 θ + cos^4 θ. Read More » Evaluate 2sec^2 θ + 3 cosec^2 θ – 2 sin θ cos θ if θ = 45. Read More » If θ is an acute angle and sin θ = cos θ, find the value of tan^2 θ + cot^2 θ – 2. Read More » Evaluate (5/cot^2 30) + (1/ sin^2 60) – cot^2 45 + 2 sin^2 90 Read More » Prove that sec A (1- sin A)(sec A + tan A) = 1 Read More » Prove that: (sin A – 2 sin^3 A)/(2cos^3 A – cos A) = tan A Read More » If A and B are acute angles such that sin(A-B) = 0 and 2 cos (A+B) -1 = 0, then find angles A and B. Read More » Evaluate (5cos^2 60 + 4 sec^2 30 – tan ^2 45) / (sin^2 30 + cos^2 30) = 1 + sin θ cos θ Read More » Prove that: cos^2 θ/(1 – tan θ) + sin^3 θ/(sin θ – cos θ) = 1 + sin θ cos θ Read More » Prove that: sin θ / (1 + cos θ) + (1 + cos θ) / sin θ = 2 cosec θ Read More » Prove that: (1/cosθ – cos θ) (1/(sin θ) – sin θ) = 1/(tan θ+ cot θ) Read More » If Cos A + Cos^2 A = 1, then find the value of Sin^2 A + Sin^4 A. Read More » If 4 cot^2 45° — sec2^ 60° + sin^2 60° + p = 3/4 then find the value of p. Read More » Prove that, 2(sin^6 θ + cos^6 θ) – 3 (sin^4 θ + cos^4 θ) +1 = 0 Read More » If tan theta = 1/root7, then show that = (cosec sq theta – sec sq theta)/(cosec sq theta + sec sq theta) = 3/4. Read More » If sin θ + sin^2 θ = 1, then prove that cos^2 θ + cos^4 θ = 1. Read More » Prove that (cosecA – sinA) (secA-cosA) = 1/(cotA+tanA) Read More » Prove that, (tanθ + secθ-1)/(tanθ – secθ + 1) = (1 + sinθ)/cosθ Read More » If Sin α = 1/√2 and Cot β = √3, then find the value of Cosec α + Cosec β. Read More » If Sin θ + Cos θ = √3, then find the value of Sin θ . Cos θ Read More »
Prove that (sin A + cos A)/(sin A – cos A) + (sin A – cos A)/(sin A + cos A) = 2/(2 sin2 A – 1) Read More »
If 2sin(A + B) = √3 and cos(A – B) = 1 , then find the measures of angles A and B. 0 <= A B, (A + B) <= 90 deg Read More »
If x = a sec(theta) + b tan theta and y = a tan theta + b sec(theta), prove that x ^ 2 – y ^ 2 = a ^ 2 – b ^ 2 Read More »
If sec α = 2/√3, then find the value of 1- cosec α /1+ cosec α , where α is in IV quadrant. Read More »
If A and B are acute angles such that sin(A-B) = 0 and 2 cos (A+B) -1 = 0, then find angles A and B. Read More »
If tan theta = 1/root7, then show that = (cosec sq theta – sec sq theta)/(cosec sq theta + sec sq theta) = 3/4. Read More »
