If Root3 Tan 2theta Plus Root3 Tan 3theta Plus Tan 2 Theta 1) nπ + π/5 2) (n + 1/6) π/5 3) (2n ± 1/6) π/5 4) (n + 1/3) π/5 Answer: (2) (n + 1/6) π/5 Solution: Given, √3 tan 2θ + √3 tan 3θ +... View Article
If 2 Sin Theta Plus Tan Theta 0 Then The General Values Of Theta 1) 2nπ ± π/3 2) nπ, 2nπ ± 2π/3 3) nπ, 2nπ ± π/3 4) nπ, nπ + 2π/3 Answer: (2) nπ, 2nπ ± 2π/3 Solution: Given, 2 sin θ + tan θ = 0... View Article
If 2 Tan Square Theta Sec Square Theta Then 1) nπ + π/4 2) nπ - π/4 3) nπ ± π/4 4) 2nπ ± π/4 Answer: (2) nπ ± π/4 Solution: Given, 2 tan2θ = sec2θ 2(sin2θ/cos2θ) = 1/cos2θ... View Article
If Sin Square Theta Minus 2 Cos Theta Plus 1 4 0 Then 1) nπ ± π/3 2) 2nπ ± π/3 3) 2nπ ± π/6 4) nπ ± π/6 Answer: (2) 2nπ ± π/3 Solution: Given, sin2θ - 2 cos θ + 1/4 = 0 Using the... View Article
If Sec Square Theta 4 3 Then The General Value Of Theta Is 1) 2nπ ± π/6 2) nπ ± π/6 3) 2nπ ± π/3 4) nπ ± π/3 Answer: (2) nπ ± π/6 Solution: Given, sec2θ = 4/3 sec θ = √(4/3) sec θ = ±2/√3... View Article
If Sin Square Theta Is 1 4 Then The Most General Value Of Theta 1) 2nπ ± (-1)n π/6 2) (nπ/2) ± (-1)n π/6 3) nπ ± π/6 4) 2nπ ± π/6 Answer: (3) nπ ± π/6 Solution: Given, sin2θ = 1/4 sin θ =... View Article
Tanh Inverse 1 2 Plus Tanh Inverse 1 3 Is 1) tanh-1(5/7) 2) tanh-1(7/5) 3) tanh-1(1/6) 4) tanh-1(5/6) Answer: (1) tanh-1(5/7) Solution: We know that, tanh-1(x) + tanh-1(y)... View Article
If Tan Theta Plus I Phi Sin X Plus Iy Then The Value Of 1) tan x cot 2θ 2) tan x sin 2θ 3) cot x sin 2θ 4) None of these Answer: (3) cot x sin 2θ Solution: Given, tan(θ + iΦ) = sin(x +... View Article
The Value Of Cosech Pi I 6 Is 1) -2 2) 2 3) -2i 4) 2i Answer: (3) -2i Solution: We know that cosech(ix) = -i cosec x cosech(Ï€i/6) = -i cosec(Ï€/6) = -i(2)... View Article
If F X Cosh X Minus Sinh X Then F X1 Plus X2 1) f(x1).f(x2)...f(xn) 2) f(x1) + f(x2) + ... +f(xn) 3) 0 4) 1 Answer: (1) f(x1).f(x2)...f(xn) Solution: Given, f(x) = cosh x -... View Article
If F Of X Is Cosh X Plus Sinh X And F Of P 1) xy 2) x - y 3) x + y 4) None of these Answer: (3) x + y Solution: Given, f(x) = cosh x + sinh x From this, we can write f(y)... View Article
Cosech X Root Of Cosech Square X Plus 1 Equals 1) tanh x 2) coth x 3) sech x 4) cosh x Answer: (3) sech x Solution: cosech x/√(cosech2x + 1) Using the identity coth2x - cosech2x... View Article
1 Plus Tanh X 1 Minus Tanh X Is 1) e2x 2) e-2x 3) i 4) -1 Answer: (1) e2x Solution: We know that tanh x = (ex - e-x)/ (ex + e-x) (1 + tanh x)/(1 - tanh x) = [1... View Article
The Value Of E Power 2 Theta Minus 1 1) coth θ 2) coth 2θ 3) tanh θ 4) tanh 2θ Answer: (3) tanh θ Solution: (e2θ - 1)/(e2θ + 1) = (eθ eθ - 1)/(eθ eθ - 1) = [eθ(eθ -... View Article
Tanh X Plus Y Equals 1) (tanh x + tanh y)/(1 - tanh x tanh y) 2) (tanh x + tanh y)/(1 + tanh x tanh y) 3) (tanh x - tanh y)/(1 - tanh x tanh y) 4) (tanh x -... View Article
Sinh 3z Equals 1) 2 sinh z - 4 sinh3z 2) 4 sinh3z - 3 sinh z 3) 3 sinh z + 4 sinh3z 4) None of these Answer: (3) 3 sinh z + 4 sinh3z Solution:... View Article
Find The Real Part Of Tan Inverse 1 Plus I 1) -(1/2) tan-1(2) 2) 12 tan-1(2) 3) -(1/2) tan-1(1/2) 4) 0 Answer: (1) -(1/2) tan-1(2) Solution: Let a + ib = tan-1(1 + i) a - ib... View Article
Value Of Tan Inverse Sin 2 Minus 1 Cos 2 Is 1) (Ï€/2) - 1 2) 1 - (Ï€/4) 3) 2 - (Ï€/2) 4) (Ï€/4) - 1 Answer: (2) 1 - (Ï€/4) Solution: We know that sin 2A = 2 sin A cos A cos 2A =... View Article
Tan 2 Tan Inverse 1 5 Minus Pi 4 Equals 1) 17/7 2) -17/7 3) 7/17 4) -7/17 Answer: (4) -7/17 Solution: 2 tan-1(1/5) = tan-1(1/5) + tan-1(1/5) Using the formula tan-1(x) +... View Article
Tan 2 Cos Inverse 3 5 Equals 1) 7/25 2) 24/25 3) -24/7 4) 8/3 Answer: (3) -24/7 Solution: Let cos-1(3/5) = A....(i) cos A = 3/5 Using the identity sin2A +... View Article