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The Most General Solution Of Root3 Cos Theta Sin Theta 2 Is

1) θ = nπ ± π/4 + π/6 2) θ = nπ ± π/4 - π/6 3) θ = 2nπ ± π/4 + π/6 4) θ = 2nπ ± π/4 - π/6 Answer: (1) θ = nπ ± π/4 + π/6 Solution:... View Article

The Root Of The Equation 1 Cos Theta Sin Theta Sin Theta 2 Is

1) kπ, k ∈ I 2) 2kπ, k ∈ I 3) k π/2, k ∈ I 4) None of these Answer: (2) 2kπ, k ∈ I Solution: Given, 1 - cos θ = sin θ . sin θ/2 2... View Article

The Most General Values Of Theta Satisfying Tan Theta Tan 3pi 4 Theta 2 Are

1) 2nπ ± π/3, n ∈ Z 2) nπ ± π/3, n ∈ Z 3) 2nπ ± π/6, n ∈ Z 4) nπ ± π/6, n ∈ Z Answer: (2) nπ ± π/3, n ∈ Z Solution: Given, tan θ +... View Article

If 3 Cos X Not Equal To 2 Sin X Then The General Solution Of Sin 2 X Cos 2x 2 Sin 2x Is

1) nπ + (-1)n π/2, n ∈ Z 2) nπ/2, n ∈ Z 3) (4n ± 1)π/2, n ∈ Z 4) (2n - 1), n ∈ Z Answer: (3) (4n ± 1)π/2, n ∈ Z Solution: sin2x - cos 2x =... View Article

General Solution Of Sin X Cos X Min Of 1 A 2 4a 6 Is

1) (nπ/2) + (-1)n π/4 2) 2nπ + (-1)n π/4 3) nπ + (-1)n + 1 π/4 4) nπ + (-1)n π/4 - π/4 Answer: (4) nπ + (-1)n π/4 - π/4 Solution:... View Article

The Solution Of The Equation Sin X Cos X Power 1 Sin 2x 2 Pi X Pi Is

1) π/2 2) π 3) π/4 4) 3π/4 5) π/3 Answer: (3) π/4 Solution: [sin x + cos x]1 + sin 2x = 2 Let us consider, sin x + cos x The... View Article

The Solution Of Trigonometric Equation Cos 4 X Sin 4 X 2 Cos 2x Pi

1) x = (nπ/2) ± sin-1(1/5) 2) x = (nπ/2) + (-1)n/4 sin-1(±2√2/3) 3) x = (nπ/2) ± cos-1(1/5) 4) x = (nπ/2) - (-1)n/4 cos-1(1/5)... View Article

The Number Of Solutions Of 2 Sin X Cos X 3 Is

1) 1 2) 2 3) infinite 4) no solution Answer: (4) no solution Solution: Given, 2 sin x + cos x = 3 The range of the equation a cos... View Article

If Sin Theta 1 2 And Tan Theta 1 Root3 For All N Belongs To I

1) 2nπ + π/6, ∀ n ϵ I 2) 2nπ + π/4, ∀ n ϵ I 3) 2nπ + π/3, ∀ n ϵ I 4) 2nπ + π/5, ∀ n ϵ I Answer:(1) 2nπ + π/6, ∀ n ϵ I Solution:... View Article

The Positive Integer Value Of N Greater Than 3 Satisfying The Equation 1 Sin Pi N

1) 8 2) 6 3) 5 4) 7 Answer: (4) 7 Solution: Given, 1/sin π/n = 1/sin 2π/n + 1/sin 3π/n (1/sin π/n) - (1/sin 3π/n) = 1/sin 2π/n... View Article

Number Of Solutions Of The Equation Tan X Sec X 2 Cos X

1) 0 2) 1 3) 2 4) 3 Answer: Solution: tan x + sec x = 2 cos x (sin x/cos x) + (1/cos x) = 2 cos x (sin x + 1) = 2 cos2x sin x +... View Article

The Number Of Real Solutions Of The Equation X 3 X 2 4x 2 Sin X 0 In 0 X 2pi Is

1) four 2) two 3) one 4) 0 Answer: (3) one Solution: Given, x3 + x2 + 4x + 2 sin x = 0....(i), 0 ≤ x ≤ 2π Let f(x) = x3 + x2 + 4x... View Article

If Log Cos X Tan X Log Sin X Cot X Then The Most General Solution X Is

1) 2nπ - 3π/4, n ϵ Z 2) 2nπ + π/4, n ϵ Z 3) nπ + π/4, n ϵ Z 4) None of these Answer: (2) 2nπ + π/4, n ϵ Z Solution: Given, logcos x tan x... View Article

The Most General Solutions Of The Equation Sec 2 X Root2 1 Tan 2 X Are

1) nπ ± π/4 2) 2 nπ + π/4 3) nπ ± π/8 4) None of these Answer: (3) nπ ± π/8 Solution: Given, sec2x = √2(1 - tan2x) tan2x + 1 = √2... View Article

The Sum Of The Solutions In 0 2pi Of The Equation Cos X Cos Pi 3 X

1) 4π 2) π 3) 2π 4) 3π Answer: (3) 2π Solution: cos x cos(π/3 - x) cos(π/3 + x) - 1/4 cos x [cos2(π/3) - sin2x] = 1/4 cos... View Article

E Log Cosh 1 2 Is Equal To

1) log (2 - √3) 2) log (√3 - 2) 3) log (2 + √3) 4) log (2 + √5) Answer: (3) log (2 + √3) Solution: We know that, cosh-1(x) = log[x... View Article

If Tanh 1 X Iy 1 2 Tanh 1 2x 1 X 2 Y2 I 2 Tan 1 2y 1 X 2 Y 2

1) i tanh-1y 2) -i tanh-1(y) 3) i tan-1y 4) -tan-1(y) Answer: (3) i tan-1(y) Solution: Given, tanh-1(x + iy) = 1/2 tanh-1[2x/(1 +... View Article

The maximum value of [latex]4 sin^{2} x + 3 cos^{2}x[/latex] is

1) 4 2) 3 3) 7 4) 5 Answer: (1) 4 Solution: 4 sin2x + 3 cos2x = sin2x + 3(sin2x + cos2x) = sin2x + 3(1) = sin2x + 3 The maximum... View Article

The Maximum Value Of Sin Theta Cos Theta In 0 Pi 2 Is

1) √2 2) 2 3) 0 4) -√2 Answer: (1) √2 Solution: The maximum value of a cos x + b sin x = √(a2 + b2) Now, sin θ + cos θ = (1).... View Article

If Y Cos 2 X Sec 2 X Then

1) y ≤ 2 2) y ≤ 1 3) y ≥ 2 4) 1 < y < 2 Answer: (3) y ≥ 2 Solution: Given, y = cos2x + sec2x Let cos2x and sec2x be the two... View Article

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