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The Value Of The Expression Sin 6 Theta Cos 6 Theta 3 Sin 2 Theta Cos 2 Theta

1) 0 2) 2 3) 3 4) 1 Answer: (4) 1 Solution: sin6θ + cos6θ + 3 sin2θ cos2θ = (sin2θ)3 + (cos2θ)3 + 3 sin2θ cos2θ = (sin2θ)3 + (cos2θ)3 +... View Article

Cos 1 Cos 2 Cos 3 Cos 180 Is Equal To

1) 1 2) 0 3) 2 4) -1 Answer: (4) -1 Solution: cos 1° + cos 2° + cos 3° + ... + cos 180° = cos 1° + cos 2° + cos 3° + .... + cos 177° +... View Article

If Sec Theta Tan Theta K Then Cos Theta Equals

1) (k2 + 1)/2k 2) 2k/(k2 + 1) 3) k/(k2 + 1) 4) k/(k2 - 1) Answer: (2) 2k/(k2 + 1) Solution: Given, sec θ + tan θ = k....(i) We know... View Article

The Value Of The Expression Cos 1 Cos 2 Cos179 Is

1) 0 2) 1 3) 1/√2 4) -1 Answer: (1) 0 Solution: cos 1° cos 2° cos 3° ... cos 179° cos 1° cos 2° cos 3° ... cos 179° = cos 1° cos 2° cos... View Article

Tan A 1 Sec A 1 Sec A Tan A Is Equal To

1) 2 sin A 2) 2 cos A 3) 2 cosec A 4) 2 sec A Answer: (3) 2 cosec A Solution: [tan A/(1 + sec A)] + [(1 + sec A)/tan A] = [(tan2A + (1 +... View Article

The Value Of Cos 270 Theta Cos 90 Theta Sin 270 Theta Cos Theta Is

1) 0 2) -1 3) 1/2 4) 1 Answer: (4) 1 Solution: cos (270° + θ) cos (90° - θ) - sin (270° - θ) cos θ = sin θ sin θ - (-cos θ) cos θ =... View Article

The Value Of Cos 480 Sin 150 Sin 600 Cos 390 Is

1) 0 2) 1 3) 1/2 4) -1 5) -1/2 Answer: (4) - 1 Solution: cos 480° sin 150° + sin 600° cos 390° cos (540° - 60°) sin (180° - 30°) + sin... View Article

The Expression Cos 10pi 13 Cos 8pi 13 Cos 3pi 13 Cos 5pi 13 Is

1) - 1 2) 0 3) 1 4) None of these Answer: (2) 0 Solution: cos 10π/13 + cos 8π/13 + cos 3π/13 + cos 5π/13 cos(π - 3π/13) + cos(π - 5π/13)... View Article

Sec 2 Theta 4xy X Y 2 Is True If And Only If

1) x + y ≠ 0 2) x = y, x ≠ 0 3) x = y 4) x ≠ 0, y ≠ 0 Answer: (2) x = y, x ≠ 0 Solution: Given, sec2θ = 4xy/(x + y)2 We know that,... View Article

The General Value Of Theta Satisfying The Equation 2sin 2theta 3sin Theta Is

1) nπ + (-1)n π/6 2) nπ + (-1)n π/2 3) nπ + (-1)n 5π/6 4) nπ + (-1)n 7π/6 Answer: (4) nπ + (-1)n 7π/6 Solution: 2 sin2θ - 3 sin θ - 2 = 0... View Article

3 Sin X Cos X 4 6 Sin X Cos X 2 4 Sin 6 X Cos 6 X Is

1) 11 2) 12 3) 13 4) 14 Answer: (3) 13 Solution: 3(sin x – cos x)4 + 6(sin x + cos x)2 + 4(sin6x + cos6x) = 3 [(sin x – cos x)2]2 +... View Article

If X Sin3 Theta Y Cos3 Theta Sin Theta Cos Theta And X Sin Theta Y Cos Theta Then X 2 Y 2 Is

1) 2 2) 0 3) 3 4) 4 5) 1 Answer: (5) 1 Solution: Given, χ sin3θ + y cos3θ = sin θ cos θ (χ sin θ) sin2θ + (y cos θ) cos2θ = sin θ cos... View Article

If Sec Theta M Tan Theta N Then 1 M Is

1) 2 2) 2m 3) 2n 4) mn Answer: (1) 2 Solution: 1/m[(m + n) + 1/(m + n)] = 1/m [{(m + n)2 + 1}/ (m + n)] = 1/m [(m2 + n2 + 2mn + 1)/ (m... View Article

Let N Be A Positive Integer Such That Sin Pi 2n Cos Pi 2n Rootn 2 Then

1) 6 ≤ n ≤ 8 2) 4 < n ≤ 8 3) 4 ≤ n ≤ 8 4) 4 < n < 8 Answer: (4) 4 < n < 8 Solution: sin(π/2n) + cos(π/2n) = √n/2 Squaring... View Article

The value of tan [latex]tan \: 67 \frac{1}{2}^o + cot \: 67 \frac{1}{2}^o[/latex] is

1) √2 2) 3√2 3) 2√2 4) 2 - √2 Answer: (3) 2√2 Solution: tan 67 1/2° + cot 67 1/2° = tan (135/2)° + cot (135/2)° Let us consider tan... View Article

Let 0 X Pi 4 Then Sec 2 X Tan 2 X Equals

(1) tan(x - π/4) (2) tan(π/4 - x) (3) tan(x + π/4) (4) tan2(x + π/4) Answer: (2) tan (π/4 - x) Solution: sec 2x - tan 2x (1/cos 2x) -... View Article

If Tan Theta 1 Root7 Then Cosec 2 Theta Sec 2 Theta Is Equal To

(1) 1/2 (2) 3/4 (3) 5/4 (4) 2 Answer: (2) ¾ Solution: Given, tan θ =1/√7 (cosec2θ - sec2θ)/ (cosec2θ + sec2θ) =[(1/sin2θ) -... View Article

Consider The Following Relations 1 A B A A Intersection Of B 2 A A Intersection Of B Union Of A B 3 A B Union Of C A B Union Of A C Which Of These Is Are Correct

1) 1 and 3 2) 2 only 3) 2 and 3 4) 1 and 2 Solution: (4) A - B = A - (A ∩ B) is correct. A = (A ∩ B) ⋃ (A - B) is correct 3. is false.... View Article

If A Is Equal To X Y Then The Power Set Of A Is Equal To

1) {xx, yy} 2) {ɸ, x, y} 3) {ɸ, {x}, {2y}} 4) {ɸ, {x}, {y}, {x, y}} Solution: (4) A = {x, y} P (A) = {ɸ, {x}, {y}, {x, y}}... View Article

If A 1 2 3 4 5 B 2 4 6 C 3 4 6 Then A Union Of B Intersection Of C Is

1) {3, 4, 6} 2) {1, 2, 3} 3) {1, 4,3} 4) None of these Solution: (1) A = {1, 2, 3, 4, 5} B = {2, 4, 6} C = {3, 4, 6} (A ⋃ B) = {1, 2,... View Article

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