View in English View in Hindi What is the value of cot 4π/3 ?

A) 1/√3

B) -√3

C) -1

D) √3

Correct Answer : 1/√3

Explanation : cot 4π/3
= cos 4π/3 / sin 4π/3
= -1/2 / -√3/2
= 1/√3

What is the value of sinx √( 1 /1+cosx + 1 /1-cosx ) ?

A) √2

B) 2√2

C) √2 tanx

D) 0

Correct Answer : √2

Explanation : sinx √( 1 /1+cosx + 1 /1-cosx )
=sinx √( 1-cosx + 1+cosx / (1+cosx ) (1-cosx) )
=sinx √( 2 / (1 - cos^{2} x ) )
=sinx √ (2 / sin^{2} x)
=sinx √ 2 / sinx
=√ 2

What is cos^{4} A - sin^{4} A / cos^{2} A - sin^{2} A equal to?

A) cos^{2} A - sin^{2} A

B) cos A - sin A

C) 1

D) 2

Correct Answer : 1

Explanation : cos^{4} A - sin^{4} A / cos^{2} A - sin^{2} A
= (cos^{2} A)^{2} - (sin^{2} A)^{2} / cos^{2} A - sin^{2} A
= (cos^{2} A + sin^{2} A) (cos^{2} A - sin^{2} A) / (cos^{2} A - sin^{2} A)
= (cos^{2} A + sin^{2} A) (cos^{2} A - sin^{2} A) / (cos^{2} A - sin^{2} A)
= (cos^{2} A + sin^{2} A)
= 1

If 7sin^{2} x +3cos^{2} x = 4, 0 < x < 90º ,then what is the value of tan x?

A) √2

B) 1

C) √3/2

D) 1/√3

Correct Answer : 1/√3

Explanation : 7sin^{2} x +3cos^{2} x = 4
7sin^{2} x/cos^{2} x + 3cos^{2} x/cos^{2} x = 4/cos^{2} x
7tan^{2} x + 3 = 4sec^{2} x
7tan^{2} x + 3 = 4(1+tan^{2} x)
3tan^{2} x = 1
tan x = 1/√3

If x = a cosθ + b sinθ and y = a sinθ - b cosθ then what is x^{2} + y^{2} equal to?

A) 2ab

B) a + b

C) a^{2} + b^{2}

D) a^{2} - b^{2}

Correct Answer : a^{2} + b^{2}

Explanation : x^{2} + y^{2 } = (a cosθ + b sinθ)^{2} + (a sinθ - b cosθ)^{2}
= (a^{2} cos^{2} θ + b^{2} sin^{2} θ + 2*ab* cosθ*sinθ) + (a^{2} cos^{2} θ + b^{2} sin^{2} θ - 2*ab* cosθ*sinθ)
= (a^{2} cos^{2} θ + b^{2} sin^{2} θ + a^{2} cos^{2} θ + b^{2} sin^{2} θ )
= a^{2} (cos^{2} θ + sin^{2} θ) + b^{2} (cos^{2} θ + sin^{2} θ)
= a^{2} + b^{2}

2 tan 45° /( 1+ tan^{2} 45°) = ?

A) sin 90°

B) tan 30°

C) tan 90°

D) sin 45°

Correct Answer : sin 90°

Explanation : 2 tan 45° /( 1+ tan^{2} 45°)
= 2 / (1 + 1^{2} ) (tan 45°=1)
= 1
= sin 90°

If sinA= 8/17 and cosA=15/17, then cotA=?

A) 17/8

B) 8/15

C) 17/15

D) 15/8

Correct Answer : 15/8

Explanation : As given sinA = 8/17 = perpendicular/hypotenuse
cosA= 15/17 = base/hypotenuse

tanA = sinA/cosA = perpendicular/base = 8/15
cotA = 1/tanA = base/perpendicular = 15/8