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If Tan Alpha 1 7 Tan Beta 1 3 Then Cos 2alpha Equals To

1) sin 2β 2) sin 4β 3) sin 3β 4) None of these Answer: (2) sin 4β Solution: Given, tan α = 1/7, tan β = 1/3 cos 2α = (1 -... View Article

Sin 3theta Cos 3theta Sin Theta Cos Theta 1

1) 2 sin 2θ 2) 2 cos 2θ 3) tan 2θ 4) cot 2θ Answer: (1) 2 sin 2θ Solution: (sin 3θ - cos 3θ)/(sin θ + cos θ) + 1 = [(3 sin θ - 4... View Article

If Cos A 3 4 Then 32 Sin A 2 Sin 5a 2 Equals To

1) 7 2) 8 3) 11 4) None of these Answer: (3) 11 Solution: Given, cos A = 3/4 32 sin (A/2) sin (5A/2) = 16 [2 sin (A/2) sin... View Article

If Tan A 1 Cos B Sin B Then Correct Relation Between Tan 2a And Tan B Is

1) tan 2A = tan B 2) tan 2A = tan2B 3) tan 2A = tan2B + 2 tan B 4) None of these Answer: (1) tan 2A = tan B Solution: Given, tan A = (1 -... View Article

If Sin Theta Plus Sin Phi A And Cos Theta Plus Cos Phi B Then

1) √[(a2 + b2)/ (4 - a2 - b2)] 2) √[(4 - a2 - b2)/ (a2 + b2)] 3) √[(a2 + b2)/ (4 + a2 + b2)] 4) √[(4 + a2 + b2)/ (a2 + b2)] Answer:... View Article

If Cos Theta Minus Alpha Cos Theta And Cos Theta Plus Alpha Are In Hp

1) ±√2 2) ±√3 3) ±1/√2 4) None of these Answer: (1) ±√2 Solution: If a, b, c are in HP, then b = 2ac/(a + c). Given, cos(θ - α),... View Article

The Value Of Tan 7 And Half Degree Is Equal To

1) √6 + √3 + √2 - 2 2) √6 - √3 + √2 - 2 3) √6 - √3 + √2 + 2 4) √6 - √3 - √2 - 2 Answer: (2) √6 - √3 + √2 - 2 Solution: sin 15° =... View Article

Sin Theta Plus Sin 2theta 1 Plus Cos Theta Plus Cos 2theta

1) (1/2) tan θ 2) (1/2) cot θ 3) tan θ 4) cot θ Answer: (3) tan θ Solution: (sin θ + sin 2θ)/(1 + cos θ + cos 2θ) Using the... View Article

2 Sin A Cos Cube A Minus 2 Sin Cube A Cos A Equals To

1) sin 4A 2) (1/2) sin 4A 3) (1/4) sin 4A 4) None of these Answer: (2) (1/2) sin 4A Solution: 2 sin A cos3A - 2 sin3A cos A = 2... View Article

Sec 2a Plus 1 Sec Square A Equals To

1) sec A 2) 2 sec A 3) sec 2A 4) 2 sec 2A Answer: (4) 2 sec 2A Solution: (sec 2A + 1)sec2A = [(1/cos 2A) + 1] (1/cos2A) = [(1 +... View Article

If Tan Square Theta Equals To 2 Tan Square Phi Plus 1 Then

1) -1 2) 0 3) 1 4) None of these Answer: (2) 0 Solution: Given, tan2θ = 2 tan2Φ + 1....(i) We know that, cos 2θ = (1 - tan2θ)/(1... View Article

If Tan X Equal To B A Then Root Of A Plus B A Minus B

1) 2 sin x/√(sin 2x) 2) 2 cos x/√(cos 2x) 3) 2 cos x/√(sin 2x) 4) 2 sin x/√(cos 2x) Answer: (2) 2 cos x/√(cos 2x) Solution: Given,... View Article

Cos Alpha Plus Cos Beta Square Plus Sin Alpha Plus Sin Beta Square

1) 4 cos2(α - β)/2 2) 4 sin2(α - β)/2 3) 4 cos2(α + β)/2 4) 4 sin2(α + β)/2 Answer: (1) 4 cos2(α - β)/2 Solution: (cos α + cos β)2... View Article

Cosec A Minus 2 Cot 2a Cos A Equals To

1) 2 sin A 2) sec A 3) 2 cos A cot A 4) None of these Answer: (1) 2 sin A Solution: cosec A - 2 cot 2A cos A = cosec A - (2 cos A/... View Article

1 Tan 3 A Minus Tan A Minus 1 Cot 3a Minus Cot A

1) tan A 2) tan 2A 3) cot A 4) cot 2A Answer: (4) cot 2A Solution: [1/(tan 3A - tan A)] - [1/(cot 3A - cot A)] = [1/(sin 3A/cos 3A... View Article

Sin 2a 1 Plus Cos 2a Cos A 1 Plus Cos A Equals To

1) tan A/2 2) cot A/2 3) sec A/2 4) cosec A/2 Answer: (1) tan A/2 Solution: [sin 2A/(1 + cos 2A)] [cos A/(1 + cos A)] Using the... View Article

If A Tan Theta Equal To B Then A Cos 2theta Plus B Sin 2theta

1) a 2) b 3) -a 4) -b Answer: (1) a Solution: Given, a tan θ = b tan θ = b/a....(i) cos 2θ = (1 - tan2θ)/(1 + tan2θ) = [1 -... View Article

If Cos 2b Cos A Plus C Cos A Minus C Then Tan A Tan B Tan C Are In

1) A.P 2) G.P 3) H.P 4) None of these Answer: (2) G.P Solution: Given, cos 2B = cos(A + C)/ cos(A - C) (1 - tan2B)/ (1 + tan2B) =... View Article

Sin 4theta Can Be Written As

1) 4 sin θ(1 - 2 sin2θ) √(1 - sin2θ) 2) 2 sin θ cos θ sin2θ 3) 4 sin θ - 6 sin3θ 4) None of these Answer: (1) 4 sin θ(1 - 2 sin2θ)... View Article

If Cos A Equals To Root3 2 Then Tan 3a

1) 0 2) 1/2 3) 1 4) ∞ Answer: (4) ∞ Solution: Given, cos A = √3/2 We know that, cos π/6 = √3/2 Therefore, A = π/6 Now, tan 3A... View Article

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