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If 2 Sec 2alpha Tan Beta Cot Beta Then One Of The Value Of Alpha Beta Is

1) π/4 2) π/2 3) π 4) nπ - π/4, n ∈ I Answer: (1) π/4 Solution: Given, 2 sec 2α = tan β + cot β 2 sec 2α = (sin β/cos β) + (cos β/sin... View Article

Solution Of The Equation 3 Tan Theta 15 Is

1) θ = nπ - π/3 2) θ = nπ + π/3 3) θ = nπ - π/4 4) θ = nπ + π/4 Answer: (4) θ = nπ + π/4 Solution: Given, 3 tan (θ - 15°) = tan (θ +... View Article

If Sin 6theta Sin 4theta Sin 2theta 0 Then Value Of Theta Is

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

The Number Of Solutions Of Cos 2theta Sin Theta In Theta 2pi Is

1) 1 2) 2 3) 3 4) 4 5) 0 Answer: (3) 3 Solution: Given, cos 2θ = sin θ in 1 - 2 sin2θ = sin θ 2 sin2θ + sin θ - 1 = 0 2 sin2θ + 2... View Article

The Value Of X In Theta Pi 2 Satisfying The Equation Sin X Cos X 1 4 Is

1) π/6 2) π/3 3) π/8 4) π/4 5) π/12 Answer: (5) π/12 Solution: Given, sin x cos x = 1/4 Multiplying by 2 on both sides, 2 sin x cos x... View Article

If Sin Theta Cos Theta 0 And 0 Theta Pi Then Theta Is

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

A Value Of Theta Satisfying Sin 5theta Sin 3theta Sin Theta 0 Such That 0 Theta Pi 2

1) π/12 2) π/6 3) π/4 4) π/2 Answer: (2) π/6 Solution: Given, sin 5θ - sin 3θ + sin θ = 0 sin 5θ + sin θ = sin 3θ 2 sin(5θ + θ)/2... View Article

The Possible Values Of Theta Belongs To 0 Pi Such That Sin Theta Sin 4theta Sin 7theta 0 Are

1) 2π/9, π/4, 4π/9, π/2, 3π/4, 8π/9 2) π/4, 5π/12, π/2, 2π/3, 3π/4, 8π/9 3) 2π/9, π/4, π/2, 2π/3, 3π/4, 35π/36 4) 2π/9, π/4, π/2, 2π/3, 3π/4,... View Article

The Value Of Theta Satisfying Cos Theta Root3 Sin Theta 2 Is

1) 30° 2) 60° 3) 45° 4) 90° Answer: (2) 60° Solution: cos θ + √3 sin θ = 2 Dividing by 2 on both sides, (1/2) (cos θ + √3 sin θ) = 2/2... View Article

If Sin 2x 4 Cos X Then X Is Equal To

1) (nπ/2) ± (π/4), n ∈ Z 2) no value 3) nπ + (-1)n (π/2), n ∈ Z 4) 2nπ ± (π/2), n ∈ Z Answer: (4) 2nπ ± (π/2), n ∈ Z Solution: sin 2x = 4... View Article

The Equation 2 Sinx E Sinx 4 0 Has

1) infinite number of real roots 2) no real roots 3) exactly one real root 4) exactly four roots Answer: (2) no real roots Solution: esin... View Article

Arcsech 1 2 Is Equal To

1) log(√3 + √2) 2) log(√3 + 1) 3) log(2 + √3) 4) None of these Answer: (3) log(2 + √3) Solution: We know that arcsech(x) = log[1 + √(1 -... View Article

2 Arctanh 1 2 Is Equal To

1) 0 2) log 2 3) log 3 4) log 4 Answer: (3) log 3 Solution: We know that, tanh-1(x) = (1/2) log |(1 + x)/(1 - x)| 2 tanh-1(1/2) = 2 ×... View Article

Arcsinh Sin Theta Is Equal To

1) log tan θ/2 2) log sin θ/2 3) log cos θ/2 4) log cot θ/2 Answer: (4) log cot θ/2 Solution: We know that, sech-1(x) = log[{1 + √(1 -... View Article

1 Tanh X 2 1 Tanh X 2 Is Equal To

1) e-x 2) ex 3) 2ex/2 4) 2e-x/2 Answer: (2) ex Solution: We know that, tanh x = (ex - e-x)/(ex + e-x) Now, [1 + tanh(x/2)]/[1... View Article

If Arcsinh 2 Arcsinh 3 X Then Cosh X Is

1) (1/2)[3√5 + 2√10] 2) (1/2)[3√5 - 2√10] 3) (1/2)[12 + 2√50] 4) (1/2)[12 - 2√50] Answer: (3) 1/2 [12 + 2√50] Solution: sinh-1(x) = ln[x +... View Article

The Curve Represented By X A Sinhtheta Coshtheta Y B Sinhtheta Is

1) a hyperbola 2) a parabola 3) an ellipse 4) a circle Answer: (1) a hyperbola Solution: Given, x = a (sinh θ + cos h θ) x/a = sinh θ +... View Article

Arcsech 1 2 Arccosech 3 4 Equals

1) loge3(2 + √2) 2) loge[(1 + √3)/3] 3) loge[(2 + √3)/3] 4) loge[(2 - √3)/3] Answer: (3) loge[(2 + √3)/3] Solution: We know that... View Article

If A B C Then Cos 2 A Cos 2 B Cos 2 C 2 Cos A Cos B Cos C Is

1) 1 2) 2 3) 0 4) 3 Answer: (1) 1 Solution: Given, A + B = C Taking “cos” on both sides, cos(A + B) = cos C Similarly, sin(A + B) = sin... View Article

For All Values Of Theta The Value Of 3 Cos Theta Cos Theta Pi 3 Lies In

1) [-2, 3] 2) [-2, 1] 3) [2, 4] 4) [1, 5] Answer: (3) [2, 4] Solution: 3 - cos θ + cos (θ + π/3) = 3 - cos θ + [cos θ cos π/3 - sin θ... View Article

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