The Value Of Sin Inverse Sin 10 Is 1) 10 2) 10 - 3π 3) 3π - 10 4) None of these Answer: (3) 3π - 10 Solution: As we know sin-1(sin x) = x when -π/2 ≤ x ≤ π/2 From... View Article
Cot Cos Inverse 7 25 Equals To 1) 25/24 2) 25/7 3) 24/25 4) None of these Answer: (4) None of these Solution: Let cos-1(7/25) = A cos A = 7/25 Using the... View Article
The Value Of Cot Cosec Inverse 5 3 Plus Tan Inverse 2 3 Is 1) 3/17 2) 4/17 3) 5/17 4) 6/17 Answer: (4) 6/17 Solution: cot[cosec-1(5/3) + tan-1(2/3)]....(i) Let cosec-1(5/3) = A cosec A =... View Article
The Domain Of Sin Inverse X Is 1) (-π, π) 2) [-1, 1] 3) (0, 2π) 4) (-∞, ∞) Answer: (2) [-1, 1] Solution: The graph of sin-1(x) or arcsin x is given as:... View Article
Tan Cos Inverse Of X Is Equal To 1) [√(1 - x2)]/x 2) x/(1 + x2) 3) [√(1 + x2)]/x 4) √(1 + x2) Answer: (1) [√(1 - x2)]/x Solution: Let cos-1(x) = θ x = cos θ... View Article
If Sin Inverse 1 3 Plus Sin Inverse 2 3 Sin Inverse X Then X Is 1) 0 2) (√5 - 4√2)/9 3) (√5 + 4√2)/9 4) π/2 Answer: (3) (√5 + 4√2)/9 Solution: Given, sin-1(1/3) + sin-1(2/3) = sin-1(x) Using... View Article
If Sin Inverese X Theta Plus Beta And Sin Inverse Y 1) sin2θ + sin2β 2) sin2θ + cos2β 3) cos2θ + cos2β 4) cos2θ + sin2β Answer: (2) sin2θ + cos2β Solution: Given, sin-1(x) = θ + β... View Article
If Sin Sin Inverse 1 5 Plus Cos Inverse X 1 Then X Is 1) 1 2) 0 3) 4/5 4) 1/5 Answer: (4) 1/5 Solution: Given, sin[sin-1(1/5) + cos-1(x)] = 1 sin-1(1/5) + cos-1(x) = sin-1(1)... View Article
If A B C Be The Angles Of A Triangle Then Sigma Cot A Cot B 1) 1 2) 2 3) -1 4) -2 Answer: (1) 1 Solution: Given, A, B, C are the angles of a triangle. A + B + C = 180° ⇒ tan A + tan B +... View Article
If A Sin 8 Theta Plus Cos 14 Theta Then For All Real Values 1) A ≥ 1 2) 0 < A ≤ 1 3) 1 < 2A ≤ 3 4) None of these Answer: (2) 0 < A ≤ 1 Solution: Given, A = sin8θ + cos14θ We know that, 0... View Article
If Alpha Belongs To 0 Pi 2 Then Root Of X Square Plus X 1) 2 tan α 2) 1 3) 2 4) sec2α Answer: (1) 2 tan α Solution: Given that α ∈ (0, π/2) Thus, tan α is positive. Let √(x2 + x) and... View Article
3 Sin 4 3pi 2 Alpha Plus Sin4 3pi Alpha Minus 2 Sin 6 Pi 2 Alpha 1) 0 2) 1 3) 3 4) sin 4α + sin 6α Answer: (2) 1 Solution: 3[sin4(3π/2 - α) + sin4(3π + α)] - 2[sin6(π/2 + α) + sin6(5π - α)] =... View Article
If X Cos Theta Y Cos Theta 2pi 3 Z Cos Theta 4pi 3 Then 1) 1 2) 2 3) 0 4) 3 cos θ Answer: (3) 0 Solution: Given, x cos θ = y cos(θ + 2π/3) = z cos(θ + 4π/3) Let x cos θ = y cos(θ +... View Article
Let Alpha Beta Be Such That Pi Alpha Minus Beta 3pi 1) -6/65 2) 3/√130 3) 6/65 4) -3/√130 Answer: (4) -3/√130 Solution: Given, sin α + sin β = -21/65....(i) cos α + cos β =... View Article
If X 1 X 2 X 3 X N Are In Ap Whose Common Difference Is Alpha Then 1) [sin(n - 1)α]/ (cos x1 cos xn) 2) sin nα/(cos x1 cos xn) 3) sin(n - 1)α cos x1 cos xn 4) sin nα cos x1 cos xn Answer: (1) [sin(n -... View Article
If Tan Theta Root 3 2 The Sum Of The Infitinite Sereies 1 2 1 Cos Theta 1) 2/3 2) √3/4 3) 5/2√2 4) 5/2 Answer: (4) 5/2 Solution: Let S = 1 + 2(1 - cos θ) + 3(1 - cos θ)2 + 4(1 - cos θ)3 + .... ∞... View Article
If Alpha Beta Gamma Delta Are The Smallest Positive Angles 1) 2√(1 - k) 2) (1/2)√(1 + k) 3) 2√(1 + k) 4) None of these Answer: (3) 2 √(1 + k) Solution: Given, α < β < γ < δ And... View Article
If Sin X Plus Sin Square X 1 Then The Value Of Expression 1) 0 2) 1 3) -1 4) 2 Answer: (2) 1 Solution: Given, sin x + sin2x = 1 sin x = 1 - sin2x sin x = cos2x....(i) cos12x + 3 cos10x... View Article
If K Sin Pi 18 Sin 5pi 18 Sin 7pi 18 Then The Numerical Value Of K Is 1) 1/4 2) 1/8 3) 1/16 4) None of these Answer: (2) 1/8 Solution: Given, k = sin π/18 sin 5π/18 sin 7π/18 k = sin 10° sin 50° sin 70°... View Article
If Sin 4 A A Plus Cos 4 A B 1 A Plus B Then The Value Of 1) 1/(a + b)3 2) a3b3/(a + b)3 3) a2b2/(a + b)2 4) None of these Answer: (1) 1/(a + b)3 Solution: sin⁴A/a + cos⁴A/b = 1/(a + b)... View Article