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Trigonometry:

 Trigonometry: In a right angled OAB, where ∠BOA = θ ,

i. sin(θ) = Perpendicular / Hypotenuse     = AB / OB ;

ii. cos(θ) = Base / Hypotenuse  = OA / OB ;

iii. tan(θ) = Perpendicular / Base = AB / OA ;

iv. cosec(θ)= 1 / sin(θ) = OB / AB ;

v. sec(θ) = 1 / cos(θ) = OB / OA ;

vi. cot(θ) = 1 / tan(θ) = OA / AB ;

 Trigonometrical Identities:

i. sin² (θ) + cos² (θ) = 1.
ii. 1 + tan² (θ) = sec² (θ) .
iii. 1 + cot² (θ) = cosec² (θ) .

Values of T-ratios:

 Angle of Elevation:

Suppose a man from a point O looks up at an object P, placed above the level of his eye. Then, the angle which the line of sight makes with the horizontal through O, is called the angle of elevation of P as seen from O.
Angle of elevation of P from O = ∠AOP.

 Angle of Depression:

Suppose a man from a point O looks down at an object P, placed below the level of his eye, then the angle which the line of sight makes with the horizontal through O, is called the angle of depression of P as seen from O.

Aptitude Questions (Trigonometry):

1. The maximum and minimum value of 8 sin θ and cos θ + 4 cos 2 θ is:

A)    4 and -4

B)    16 and -16

C)    4√2 and -4√2

D)    8 and -8

E)    None of these

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2. Solve cos θ + sin θ = √2, then the value of θ is:

A)    π/3

B)    π/4

C)    π/6

D)    π/2

E)    None of these

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3. The value of  (sin135º– cos120º) / (sin135º+cos120º)  is

A)    2 + 3√2

B)    2 – 3√2

C)    3 – 2√2

D)    3 + 2√2

E)    None of these

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4. The value of is (tan47º + tan43º) / (1-tan47ºtan43º) is

A)    1

B)    ∝

C)    0

D)    -1

E)    None of these

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5. If A – B = π/3, then the value of cos A cos B + sin A sin B is

A)    ½

B)    1

C)    3/2

D)    0

E)    None of these

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