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The Sum Of The Series Sum N 1 Infinity Sin N Factorial Pi 720 Is

1) sin(π/180) + sin(π/360) + sin(π/540) 2) sin(π/6) + sin(π/30) + sin(π/120) + sin(π/360) 3) sin(π/6) + sin(π/30) + sin(π/120) + sin(π/360) +... View Article

If Cos 2x Root2 1 Cos X 1 Root2 Cos X 1 2

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

If Cos Theta 4 Sin Theta 1 Then Sin Theta 4 Cos Theta Is

1) ±1 2) 0 3) ±2 4) 4 Answer: (4) 4 Solution: Given, cos θ - 4 sin θ = 1....(i) Let us consider sin θ + 4 cos θ = x....(ii) Squaring... View Article

The Number Of Values Of Theta In The Interval Pi Pi Satisfying The Equations Cos Theta

1) 1 2) 2 3) 3 4) 4 Answer: (4) 4 Solution: Given, cos θ + sin 2θ = 0 cos θ + 2 sin θ cos θ = 0 cos θ(1 + 2 sin θ) = 0 cos θ = 0, 1 +... View Article

If Tan 3theta 1 Tan 3theta 1 Root3 Then The General Value Of Theta Is

1) (nπ/3) - (π/12) 2) nπ + (7π/12) 3) (nπ/3) + (7π/36) 4) nπ + (π/12) Answer: (3) (nπ/3) + (7π/36) Solution: Given, (tan 3θ - 1)/(tan 3θ... View Article

The Solution Of Equations Cos 2 Theta Sin Theta 1 0 Lies

1) (-π/4, π/4) 2) (π/4, 3π/4) 3) (3π/4, 5π/4) 4) (5π/4, 7π/4) Answer: (4) (5π/4, 7π/4) Solution: Given, cos2θ + sin θ + 1 = 0 ⇒ (1 –... View Article

If Cot X Cosec X Root3 Then The Principal Value

1) π/3 2) π/4 3) π/2 4) π/6 Answer: (4) π/6 Solution: Given, cot x + cosec x = √3 (cos x/sin x) + (1/sin x) = √3 (cos x + 1)/sin x =... View Article

The Number Of Solutions Of The Equation Sin 2x Cos 4x 2 Is

1) 0 2) 1 3) 2 4) ∞ Answer: (1) 0 Solution: Given, sin 2x + cos 4x = 2 sin 2x + [1 - 2 sin2(2x)] - 2 = 0 {since cos 2A = 1 - 2sin2A}... View Article

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

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

If 1 Sin Theta Sin 2 Theta 4 2root3 0 Theta Pi

1) θ = π/3 2) θ = π/6 3) θ = π/3 or π/6 4) θ = π/3 or 2π/3 Answer: (4) θ = π/3 or 2π/3 Solution: Given, 1 + sin θ + sin2θ +... = 4 + 2√3... View Article

The Number Of Solutions Of The Equation Sin X Cos 3x Sin 3x Cos 5x

1) 3 2) 4 3) 5 4) 6 Answer: (3) 5 Solution: Given, sin x cos 3x = sin 3x cos 5x 2 sin x cos 3x = 2 sin 3x cos 5x sin(x + 3x) + sin(x -... View Article

Number Of Solutions Of X 1 Cos X Is

1) 2 2) 3 3) 4 4) None of the above Answer: (1) 2 Solution: Given, |x - 1| = cos x Let y1 = |x - 1| and y2 = cos x be the two... View Article

Cos 2x 7 1 2 Sin X Can Have A Real Solution For

1) all values of a 2) a ϵ [2, 6] 3) a ϵ (-∞, 2) 4) a ϵ (0,∞) Answer: (2) a ϵ [2, 6] Solution: Given, cos 2x + 7 = 1(2 - sin x) 1 − 2... View Article

The General Solution Of Sin 3x Sin X 3 Sin 2x Cos 3x Cos X 3 Cos 2x Is

1) (nπ/2) + (π/8) for n integer 2) (nπ/2) - (π/8) for n integer 3) nπ + (π/6) for n integer 4) nπ - (π/6) for n integer Answer: (1) (nπ/2) +... View Article

The Number Of Solutions Of The Equation 1 Cos 2x Cos 2x Cot 2 X 0

1) 3 2) 2 3) 1 4) 0 Answer: (4) 0 Solution: Given, (1 - cos 2x) (cos 2x + cot2x) = 0, 0 ≤ x ≤ 2π 1 - cos 2x = 0 cos 2x = 1 That... View Article

The Minimum Value Of F X Sin 4 X Cos 4 X 0 X Pi 2 Is

1) 1/2√2 2) 1/4 3) -1/2 4) 1/2 Answer: (4) 1/2 Solution: Given, f(x) = sin4x + cos4x = (sin2x)2 + (cos2x)2 = (sin2x + cos2x) - 2... View Article

If A B C Pi Then Sin 2a Sin 2b Sin 2c Is Equal To

1) 4 sin A sin B sin C 2) 4 cos A cos B cos C 3) 2 cos A cos B cos C 4) 2 sin A sin B sin C Answer: (1) 4 sin A sin B sin C Solution:... View Article

The Maximum Value Of 4 Sin 2 X 12 Sin X 7 Is

The maximum value of 4 sin2x - 12 sinx + 7 is 1) 25 2) 4 3) does not exist 4) None of these Answer: (4) None of these Solution: 4 sin2x... View Article

In Triangle Abc If Sin 2 A Sin 2 B Sin 2 C 2 Then

1) right angle but need not be isosceles 2) right angled and isosceles 3) isosceles but need not be right angled 4) equilateral Answer: (1)... View Article

The Smallest Value Of 5 Cos Theta 12 Is

1) 5 2) 12 3) 7 4) 17 Answer: (3) 7 Solution: We know that, −1 ≤ cos θ ≤ 1 Multiplying by 5, −5 ≤ 5 cos θ ≤ 5 Adding 12, −5 + 12 ≤ 5... View Article

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