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If Sin X 3alpha 3 Sin Alpha X Then

1) tan x = tan α 2) tan x = tan2α 3) tan x = tan3α 4) tan x = 3 tan α Answer: (3) tan x = tan3α Solution: Given, sin(x + 3α) = 3... View Article

Sin 47 Sin 61 Sin 11 Sin 25 Is Equal To

1) sin 7° 2) cos 7° 3) sin 36° 4) cos 36° Answer: (2) cos 7° Solution: sin 47° + sin 61° - sin 11° - sin 25° = (sin 47° - sin 25°)... View Article

If Cos X Cos X 2y Lambda Then Tan X Y Tan Y Is

1) (1 + λ)/(1 - λ) 2) (1 - λ)/(1 + λ) 3) λ/(1 + λ) 4) λ/(1 - λ) Answer: (2) (1 - λ)/(1 + λ) Solution: Given, cos x/cos(x - 2y) =... View Article

The Value Of Cos 2 A B Cos 2 B 2 Cos A B Cos A Cos B Is

1) sin A 2) sin2A 3) cos2A 4) cos A Answer: (2) sin2A Solution: cos2(A - B) + cos2B - 2 cos(A - B) cos A cos B = cos2(A - B) + cos2B -... View Article

If Alpha Beta And Gamma Belongs To 0 Pi 2 Then

1) < 1 2) = -1 3) < 0 4) None of these Answer: (1) < 1 Solution: Let us consider, sin α + sin β + sin γ − sin(α + β + γ)... View Article

If Tan Alpha K Cot Beta Then Cos Alpha Beta

1) (1 + k)/(1 - k) 2) (1 - k)/(1 + k) 3) (k + 1)/(k - 1) 4) (k - 1)/(k + 1) Answer: (1) (1 + k)/(1 - k) Solution: Given, tan α - k... View Article

If A B 45 Then Cot A 1 Cot B 1 Is

1) 3 2) 1/2 3) - 1 4) - 2 5) 2 Answer: (5) 2 Solution: Given, A + B = 45° Taking “cot” on both sides, cot(A + B) = cot 45° (cot A cot... View Article

If Tan A And Tan B Are The Roots Of Abx 2 C 2 X Ab 0 Where A B C Are Sides Of Triangle Abc Then

1) 1 2) 3 3) 4 4) 2 5) 5 Answer: (4) 2 Solution: Given, tan A and tan B are the roots of abx2 - c2x + ab = 0. Also, a, b and c are the... View Article

The Value Of Sin 50 Sin 70 Sin 10 Is

1) 0 2) 1 3) 1/2 4) 1/√2 Answer: (1) 0 Solution: sin 50° - sin 70° + sin 10° = sin(60° - 10°) - sin(60° + 10°) + sin 10° = sin 60° cos... View Article

The Value Of Tan 40 Tan 20 Root3 Tan 20 Tan 40 Is

1) √12 2) 1/√3 3) √3 4) √3/2 Answer: (3) √3 Solution: 60° = 40° + 20° Taking “tan” on both sides, tan 60° = tan(40° + 20°) √3 = (tan 40°... View Article

Tan 81 Tan 63 Tan 27 Tan 9 Equals

1) 6 2) 0 3) 2 4) 4 Answer: (4) 4 Solution: tan 81° - tan 63° - tan 27° + tan 9° tan(90° - 9°) + tan 9° - [tan(90° - 27°) + tan... View Article

If Sin Theta Sin Alpha Then

1) (θ + α)/2 is any odd multiple of π/2 and (θ - α)/2 is any multiple of π 2) (θ + α)/2 is any odd multiple of π and (θ - α)/2 is any multiple... View Article

If Sin Theta Cosec Theta 2 Then Sin 10 Theta Cosec 10 Theta Is

1) 2 2) 210 3) 29 4) 10 Answer: (1) 2 Solution: Given, sin θ + cosec θ = 2 sin θ + (1/sin θ) - 2 = 0 sin2θ + 1 - 2 sin θ = 0 (sin θ -... View Article

If 12 Cot 2 Theta 31 Cosec Theta 32 0 Then The Value Of Sin Theta

1) 3/5 or 1 2) 2/3 or - (2/3) 3) 4/5 or 3/4 4) ± 1/2 Answer: (3) 4/5 or 3/4 Solution: 12 cot2θ – 31 cosec θ + 32 = 0 12(cos2θ/sin2θ) -... View Article

If Theta Belongs To 0 Pi 4 And T1 Tan Theta Tan Theta T2 Tan Theta Cot Theta

1) t1 > t2 > t3 > t4 2) t4 > t3 > t1 > t2 3) t3 > t1 > t2 > t4 4) t2 > t3 > t1 > t4 Answer: (2) t4 >... View Article

Sin 2 17 Point 5 Degrees Sin 2 72 Point 5 Degrees Is Equal To

1) cos290° 2) tan245° 3) cos230° 4) sin245° Answer: (2) tan245° Solution: sin217.5° + sin272.5° = sin217.5° + sin2(90° - 17.5°) =... View Article

If Cos X Cos 2 X 1 Then The Value Of Sin 12 X 3 Sin 10 X 3 Sin 8 X Sin 6 X 1

1) 2 2) 1 3) - 1 4) 0 Answer: (4) 0 Solution: Given, cos x + cos2x = 1 cos x = 1 - cos2x cos x = sin2x....(i) Let us take the given... View Article

Why Is The Second Law Of Thermodynamics Called Directional Law

In nature, the heat only moves from warmer systems to cooler systems and never the other way round. Because the flow of heat follows a specific... View Article

Does The First Law Of Thermodynamics Apply To Open Systems

The first law of thermodynamics is a universal law and can be applied to both open and closed systems.... View Article

Can The First Law Of Thermodynamics Be Violated

The first law of thermodynamics cannot be violated as the the total energy of the system is constant and the law is known to apply to all known... View Article