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For N Belongs To Z The General Solution Of Root3 1 Sin Theta Root3 1 Cos Theta 2 Is

1) θ = 2nπ ± π/4 + π/12 2) θ = nπ + (-1)n π/4 + π/12 3) θ = 2nπ ± π/4 - π/12 4) θ = nπ + (-1)n π/4 - π/12 Answer: (1) θ = 2nπ ± π/4 + π/12... View Article

If 4 Sin 2 X 8 Sin X 3 Less Than Or Equal 0 Then

1) [0, π/6] 2) [0, 5π/6] 3) [5π/6, 2π] 4) [π/6, 5π/6] Answer: (4) [π/6, 5π/6] Solution: Given, 4 sin2x – 8 sin x + 3 ≤ 0 4 sin2x - 6 sin x -... View Article

The Set Of Values Of X For Which Sin X Cos 3 X Greater Than Cos X Sin 3 X

1) (0, π/4) 2) (π/2, 3π/4) 3) (π, 5π/4) 4) (3π/2, 7π/4) Answer: (1) (0, π/4) Solution: Given, sin x cos3x > cos x sin3x, 0 ≤ x ≤ π sin x... View Article

The Most General Solutions Of 2 Sin X 2 Cos X 2 1 1 Root2 Are

1) nπ - π/4 2) nπ + π/4 3) nπ + (-1)n π/4 4) 2nπ ± π/4 Answer: (4) 2nπ ± π/4 Solution: Given, 2sin x + 2cos x = 21 - 1-/√2 2sinx + 2cosx = 2... View Article

The Number Of Real Solutions Of Sin E X Cos E X

1) 0 2) 1 3) 2 4) ∞ Answer: (1) 0 Solution: Given, sin ex . cos ex = 2x - 2 + 2-x - 2 2 sin ex cos ex = 2x - 1 + 2-x-1 sin 2ex = 2x - 1 +... View Article

If Cos Sin X Is 1 Root2 Then X Must Lies In The Interval

1) (π/4, π/2) or (π/2, π) 2) (-π/4, 0) 3) (π, 3π/2) 4) (3π/2, 2π) Answer: (1) (π/4, π/2) or (π/2, π) Solution: Given, cos(sin x) = 1/√2... View Article

A Solution Of The Equation 1 Tan Theta 1 Tan Theta Sec 2 Theta 2 Tan 2 Theta

1) θ = 0 2) θ = π/3 or -π/3 3) θ = -π/6 4) θ = π/6 Answer: (2) θ = π/3 or -π/3 Solution: Given, (1 - tan θ)(1 + tan θ)sec2θ + 2^(tan2θ) = 0... View Article

If X Sin Alpha Y Cos Alpha Then X Sec 2alpha Y Cosec 2alpha Is

1) x 2) y 3) x + y 4) x - y Answer: (1) x Solution: Given, x sin α = y cos α....(i) (x/sec 2α) + (y/cosec 2α) = x cos 2α + y sin 2α = x(1 - 2... View Article

If X Sin 6 Theta Cos 6 Theta Then X Belongs To The Interval

1) [3/4, 5/4] 2) [1/2, 3/4] 3) [1/4, 1] 4) None of these Answer: (3) [¼, 1] Solution: Given, x = sin6θ + cos6θ = (sin2θ)3 + (cos2θ)3 Using... View Article

If Cos Alpha Beta Sin Gamma Delta Is Cos Alpha Beta Sin Gamma Delta Then

1) cot α cot β = cot γ cot δ 2) cot α cot β cot γ = cot δ 3) cot α = cot β cot γ cot δ 4) None of these Answer: (2) cot α cot β cot γ = cot δ... View Article

If Cos A Minus B Cos A Plus B Cos C Plus D Cos C Minus D Then

1) tan A tan B = tan C tan D 2) tan A tan B = -tan C tan D 3) tan A tan B tan C tan D = -1 4) None of these Answer: (3) tan A tan B tan C tan... View Article

If Cot A Root Ac Cot B Root C A Cot C Root A 3 C

1) A + B = C 2) B + C = A 3) C + A = B 4) None of these Answer: (1) A + B = C Solution: Given, cot A = √ac, cot B = √(c/a), cot C = √(a3/c),... View Article

If Alpha Beta 90 Degrees Then Maximum Value Of Sin Alpha Sin Beta Is

1) 1 2) 1/2 3) 2 4) None of these Answer: (2) 1/2 Solution: Given, α + β = 90° sin α sin β = sin α sin(90° - α) = sin α cos α = (1/2) (2 sin... View Article

If 3 Tan Theta Tan Phi Is 1 Then

1) cos(θ + φ) = cos(θ - φ) 2) cos(θ + φ) = 2 cos(θ - φ) 3) cos(θ + φ) = - cos(θ - φ) 4) 2 cos(θ + φ) = cos(θ - φ) Answer:(2) cos(θ + φ) = 2... View Article

If Sin Alpha Sin Beta Cos Alpha Cos Beta 1 0 Then

1) cot α + cot β = 0 2) 1 + cot α cot β = 0 3) 1 + tan α tan β = 0 4) none of these Answer: (4) None of these Solution: Given, sin α sin β –... View Article

If 3 Sin Theta 5 Cos Theta 5 Then 5 Sin Theta 3 Cos Theta Is

1) 4 2) ±3 3) 5 4) None of these Answer: (2) ±3 Solution: Given, 3 sin θ + 5 cos θ = 5....(i) Let 5 sin θ - 3 cos θ = p....(ii) Squaring and... View Article

If Tan 2 Theta 1 E 2 Then Sec Theta Tan 3 Theta Cosec Theta Is Equal To

1) √(2 - e2) 2) (2 - e2)3/2 3) 2 - e2 4) None of these Answer: (1) (2 - e2)3/2 Solution: Given, tan2θ = 1 - e2 sec θ + tan3θ cosec θ = sec... View Article

If Pi Theta 3pi 2 The Expression Root Of 4 Sin 4 Theta 2 Sin 2 2 Theta 4 Cos 2 Pi 4 Theta 2 Is

1) 2 2) 2 + 4 sin θ 3) 2 - 4 sin θ 4) None of these Answer: (1) 2 Solution: Given, π < θ < 3π/2 Here, sin θ is negative. Now, √(4 sin4θ... View Article

If Tan Theta Plus Tan Theta Pi 3 Plus Tan Theta Pi 3 K Tan 3theta Then K Is

1) 1 2) 3 3) 1/3 4) None of these Answer: (2) 3 Solution: Given, tan θ + tan(θ + π/3) + tan(θ - π/3) = K tan 3θ LHS = tan θ + tan(θ + π/3) +... View Article

If X Sin Theta Y Sin Theta 2pi 3 Z Sin Theta 4pi 3 Then Xy Yz Zx Is

1) 1 2) 1/2 3) 0 4) None of these Answer: (3) 0 Solution: Given, x sin θ = y sin(θ + 2π/3) = z sin(θ + 4π/3) Consider, x sin θ = y sin(θ +... View Article

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