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NDA Exam Mathematics Study Material

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Trigonometry

Fill in the blank: sin A = ....... x cos A

a) Cos A
b) Cot A
c) Tan A
d) Sin A

✔Answer

✔Solution

Correct Answer Is : Tan A

Solution Is : Sin A = X * cos A X = sin A / cos A = tan A

Find the value of sin²30 cos245 + 4 tan230 + (1/2) sin290 - 2 cos290 + 1/24 .

a) 3
b) 4
c) 2
d) 1

✔Answer

✔Solution

Correct Answer Is : 2

Solution Is : Sin²30 cos²45 + 4 tan²30 + (1/2) sin²90 - 2 cos²90 + 1/24 = (1/2/2 x (1/√2)2 + 4 (1/√3)2 + (1/2) (1)2 - 2 (0)2 + 1/24 = 1/4 ( 1/2) + 4 (1/3) + (1/2) + 1/24 = 1/8 + 4/3 +1/2 + 1/24 = ( 3 + 32 + 12 +1 ) / 24 = 48 / 24 = 2

If secθ + cosec (90o - θ) = 4 , ( 0<θ<90o), then the value of tanθ is

a) √3
b) 1/√2
c) 1/√3
d) 1

✔Answer

✔Solution

Correct Answer Is : √3

Solution Is :

The numerical values of 9/cosec²θ + 4 cos²θ + 5 / (1+tan²θ) is

a) 4
b) 5
c) 9
d) 1

✔Answer

✔Solution

Correct Answer Is : 9

Solution Is :

The value of sin 39° / cos 51° + 2 tan 11° tan 31° tan 45° tan 59° tan 79° -3 (sin² 21° + sin² 69° ) is

a) 2
b) -1
c) 1
d) 0

✔Answer

✔Solution

Correct Answer Is : 0

Solution Is :

The angles of evaluation of the top of a building and the top of the chimney on the roof of the building from a point on the ground are x and 45°, respectively. The height of building is h m. Then, the height of the chimney is (in m).

a) H cot x + h
b) H cot x - h
c) H tan x - h
d) H tan x + h

✔Answer

✔Solution

Correct Answer Is : H cot x - h

Solution Is :

a) -4
b) 4
c) ±4
d) ±2

✔Answer

✔Solution

Correct Answer Is : ±4

Solution Is :

a) 25/4 sq cm
b) 25/√3 sq cm
c) 25√3/sq cm
d) 25√3 sq cm

✔Answer

✔Solution

Correct Answer Is : 25√3/sq cm

Solution Is :

a) 30°
b) 45°
c) 60°
d) None of these

✔Answer

✔Solution

Correct Answer Is : 60°

Solution Is :

If A = tan 11° tan 29° B = 2 cot 61° cot 79° , then

a) A = 2B
b) A = -2B
c) 2A = B
d) 2A = -B

✔Answer

✔Solution

NDA Exam Mathematics Study Material

Trigonometry

Fill in the blank: sin A = ....... x cos A

Correct Answer Is : Tan A

Solution Is : Sin A = X * cos A X = sin A / cos A = tan A

Find the value of sin230 cos245 + 4 tan230 + (1/2) sin290 - 2 cos290 + 1/24 .

Correct Answer Is : 2

Solution Is : Sin230 cos245 + 4 tan230 + (1/2) sin290 - 2 cos290 + 1/24 = (1/2/2 x (1/√2)2 + 4 (1/√3)2 + (1/2) (1)2 - 2 (0)2 + 1/24 = 1/4 ( 1/2) + 4 (1/3) + (1/2) + 1/24 = 1/8 + 4/3 +1/2 + 1/24 = ( 3 + 32 + 12 +1 ) / 24 = 48 / 24 = 2

If secθ + cosec (90o - θ) = 4 , ( 0<θ<90o), then the value of tanθ is

Correct Answer Is : √3

Solution Is :

The numerical values of 9/cosec2θ + 4 cos2θ + 5 / (1+tan2θ) is

Correct Answer Is : 9

Solution Is :

The value of sin 39° / cos 51° + 2 tan 11° tan 31° tan 45° tan 59° tan 79° -3 (sin2 21° + sin2 69° ) is

Correct Answer Is : 0

Solution Is :

The angles of evaluation of the top of a building and the top of the chimney on the roof of the building from a point on the ground are x and 45°, respectively. The height of building is h m. Then, the height of the chimney is (in m).

Correct Answer Is : H cot x - h

Solution Is :

Correct Answer Is : ±4

Solution Is :

Correct Answer Is : 25√3/sq cm

Solution Is :

Correct Answer Is : 60°

Solution Is :

If A = tan 11° tan 29° B = 2 cot 61° cot 79° , then

Correct Answer Is : 2A = B

Solution Is :

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Find the value of sin²30 cos245 + 4 tan230 + (1/2) sin290 - 2 cos290 + 1/24 .

Solution Is : Sin²30 cos²45 + 4 tan²30 + (1/2) sin²90 - 2 cos²90 + 1/24 = (1/2/2 x (1/√2)2 + 4 (1/√3)2 + (1/2) (1)2 - 2 (0)2 + 1/24 = 1/4 ( 1/2) + 4 (1/3) + (1/2) + 1/24 = 1/8 + 4/3 +1/2 + 1/24 = ( 3 + 32 + 12 +1 ) / 24 = 48 / 24 = 2

The numerical values of 9/cosec²θ + 4 cos²θ + 5 / (1+tan²θ) is

The value of sin 39° / cos 51° + 2 tan 11° tan 31° tan 45° tan 59° tan 79° -3 (sin² 21° + sin² 69° ) is