objective trigonometry level 1(2015)

7/21/2019 Objective Trigonometry Level 1(2015)

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Single Answer Type (Level 1)

1. If

1tan

2 2

θ =

, then the value of

sinθ is

(a)

4

5

(b)

3

5

(c)

1

2

(d)

1

2. If

5 2sec x θ = + and

5 tan y θ = + then

( ) ( )2 2

5 5 x y− − − is equal to

(a) 3 (b) 1 (c) 0 (d) 4

3. The value of

tan15 tan 75° + °is

a)

2 3

(b)4

(c)

2 3

(d)

4 3

4. If

( )sin , 1nθ φ + ≠

then the value of

tan

tan

θ

φ

is

(a)

1

n

n − (b)

1

1

n

n

+−

(c)

1

n

n− (d)

1

1

n

n

−+

5. If

0 2 x π ≤ ≤, then the numbe of solutions of the equation

! "sin cos 1 x x+ =

is

(a) 2 (b) 3 (c) 4 (d) 5

". If

2cot tan cos

3 3 3

x x kxec+ =

, then the value of

k is

(a) 1 (b) 2 (c) 3 (d)1−

7. If

3,

2 2

π π θ

∈ ÷

, then the value of

4 2 24 cos sin 2 2 cot 2 cos

4 2

π θ θ θ θ

+ + − ÷

is

(a)

2cotθ − (b)

2cotθ (c)

2cosθ (d)

2sinθ

!. The numbe of eal solutions of the equation

( ) ( )2sin cos 0 x x x x− − =is

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

#. If in a ABC ∆ ,

2 2 2 2

cos 0a A b c− − = then

(a)

4 2 A

π π < <

(b)

2 A

π π < <

(c)

2 A

π =

(d)

4 A

π <



10.

{ } 3

$ cos sin 0,2

x R x x π ∈ ≥ ∩

(a)

3 30, ,

4 4 2

π π π ∪ (b)

30, ,

4 2 2

π π π ∪ (c)

5 30, ,

4 4 2

π π π ∪ (d)

30,

2

π

11. The minimum value of

2cos sin

sin 2θ θ θ + +fo

0, 2

π θ

∈ ÷

is

(a)

2 2+ (b)

2 (c)

1 2+ (d)

2 2

12. If

( )tan 33 x y+ = and

tan 3 x = , then

tan y

is

(a)

33

10 (b)

3

10 (c)

""

10 (d)

"

10

13. The numbe of solutions of the equation

( )1cot cot % 0 2sin

x x x x

π = + ≤ ≤

is

(a) 0 (b) 1 (c) 2 (d) 3

14.

2 2

sin sin 3

sin cos

x x

x x

−−

is equal to

(a)

2sin x− (b)

2

sin x(c)

1

sin x (d)

2sin x

15. In

ABC ∆

( )cosec sin .cos cos .sin A B C B C + =

(a) 0 (b) 1 (c)1−

(d) none of these

1". The value of

tan1 tan!#° + °is

(a)

2

sin2° (b)

1

sin2° (c)

1

sin1° (d)

2

sin1°

17. If

1sin sin

2

x y+ =

andcos cos 1 x y+ =

, then( )tan x y+ =

(a)

3

4−

(b)

4

3 (c)

!

3 (d)

!

3

−



1!. If

1tan

2θ =

and

1tan

3φ =

, then

θ φ + is

(a)"

π

(b)

π (c)

0 (d)

4

π

1#. The value of

tan1 . tan 2 .tan3 ....tan!#° ° ° °

is

(a) 0 (b) 1 (c)

1

2 (d) none of these

20. If

1tan and tan , then

1 2 1

m

m mα β α β = = + =

+ +

(a)2

π

(b)3

π

(c)"

π

(d)4

π

21. The value ofcos1 .cos2 .cos3 ....cos17#° ° ° °

is

(a)

1

2

(b) 0 (c) 1 (d)1−

22. The value of

2

2

1 tan 15

1 tan 15

− °+ °

is

(a) 1 (b)3

(c)

3

2 (d) 2

23. If

( )1 1

tan , tan , then tan 22 3

A A Bβ = = + =

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

24. If

sin cos 1θ θ + = , then the value of

sin2θ is

(a) 1 (b)

1

2 (c) 0 (d)

1−

25. If

4

π α β + =

, then the value of

( ) ( )1 tan 1 tanα β + + is

(a) 1 (b) 2 (c)2−

(d) none of these



2". The value of

sin 20 sin 40 sin "0 sin!0° ° ° ° is

(a)

3

1"−

(b)

5

1" (c)

3

1" (d)

1

1"

27. The value of

2 4 !cos .cos .cos .cos

5 5 5 5

π π π π

is

(a) 1 (b) 0 (c)

1

!−

(d)

1

1"−

2!. The value of

13sin .sin

10 10

π π

is

(a)

1

2 (b)

1

2−

(c)

1

4−

(d) 1

2#. The value of

2 2cos 4! sin 12° − °

(a)

5 1

!

+

(b)

5 1

!

−

(c)

5 1

5

+

(d)

5 1

2 2

+

30. The value of

tan# tan27 tan"3 tan!1° − ° − ° + °

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

Integer Type(Integral Answers frm ! t " )

1. If

1 5 7sin .sin .sin

1! 1! 1!k

π π π =

, then k is

2. If

4 4sin cosec 2, then sin cosecθ θ θ θ + = + =

3.

( ) ( ) ( )4 2 " "3 sin cos " sin cos 4 sin cos x x x x x x− + + + +

is a t&o di'it numbe, then the sum of di'its is

4. If

3 5 7 11 cos 1 cos 1 cos 1 cos

! ! ! ! n

π π π π + + + + = ÷ ÷ ÷ ÷

, then n is

5. The numbe of solutions of

[ ]2 22 tan sec 2 in 0, 2 x x π + =

is

".

3cosec20 sec20° − ° =

7. If

tan tan 2 3 tan tan 2 3θ θ θ θ + + = , such that

3

n

k k

π π θ = +

, then k



!. umbe of solutions of the equation

tan sec 2cos x x x+ = l*in' in

[ ]0,2π

is

#. If + lies in second quadant and

3tan 4 0 A + =, and value of

2cot+ 5cos+ sin+ a

b− + =

, then

a

b

(.-

is the 'eatest inte'e function

) is

10. The value of

( ) ( )sin 45 cos 45θ θ ° + − ° − is

+ns&es

1.a 2. d 3. b 4. b 5. d ". b 7. b !. c #. b 10.

11. a 12. b 13. b 14. d 15. b 1". a 17. b 1!. d 1#. b 20.

21. b 22. c 23. c 24. c 25. b 2". c 27. d 2!. c 2#. a 30.

Inte'e T*e/..

1.! 2. 2 3. 4 4. ! 5. 4 ". 4 7. 3

!. 2 #. 2 10. 0

objective trigonometry level 1(2015)

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