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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

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

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

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

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

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

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

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

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

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 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

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

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

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

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

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

1) -5 2) 5 3) 9/4 4) 4/9 Answer: (4) 4/9 Solution: Given, tan A/2 = 3/2 We know that, cos A = 2 cos2(A/2) - 1 cos A = 1 - 2... View Article

1) f (x) > 0 ∀ x ∈ R 2) f (x) < 0 ∀ x ∈ R 3) f (x) = 0 ∀ x ∈ R 4) f (x) < x2 ∀ x ∈ R Solution: (1) f (x) > 0 ∀ x ∈ R... View Article

1) y / x 2) x / y 3) my / nx 4) ny / mx Solution: (3) my / nx Let xm= u, yn = v un + vv^v = z uz = vz = z u = v = z1/2 xm =... View Article

1) 1 2) –1 3) 0 4) None of these Solution: (3) 0... View Article