Model Question Paper

Trigonometry - Part IV
10th Standard

Maths Reg.No. :            

I.Answer all the questions.

II.Use blue pen only.
III.Question number 16 is compulsory.
Time : 01:00:00 Hrs Total Marks : 40
Part-A 5x1=5
1) 2
(1 + cot θ) (1 − cosθ) (1 + cosθ) =

(a) 2
tan θ − sec θ
2
(b) 2
sin θ − cos θ
2
(c) 2
sec θ − tan θ
2
(d) 2
cos θ − sin θ
2

2) 2
(cos θ − 1) (cot θ + 1) + 1 =
2

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

2

3) 1+tan θ

2
=
1+cot θ

(a) cos θ
2
(b) tan θ
2
(c) sin θ
2
(d) cot θ
2

4) 2
sin θ +
1

2
=
1+tan θ

(a) cosec θ + cot θ

2 2
(b) 2
cosec θ − cot θ
2
(c) 2
cot θ − cosec θ
2
(d) 2
sin θ − cos θ
2

5) 2
9tan θ − 9sec θ =
2

(a) 1 (b) 0 (c) 9 (d) -9

Part-B 5 x 2 = 10
6) Prove the following identities sin θ
= cosec θ + cot θ
1−cos θ
−−−−−
7) Prove the following identities √ 1−sin θ
= sec θ − tan θ
1+sin θ

8) Prove the following identities cos θ

= 1 + sin θ
secθ−tan θ
−−−− −− −−−− −− −
9) Prove the following identities √ sec 2 2
 θ + cosec  θ = tan θ + cot θ
2

10) Prove the following identities 1+cos θ−sin  θ

= cotθ
sin θ (1+cos θ)

Part-C 5 x 5 = 25
11) Prove the following identities.   (1 + cot θ − cosec θ)(1 + tanθ + sec θ) = 2 
12) Prove the following identities.    
sin θ−cos θ+1 1
=
sin θ+cos θ−1 sec θ−tan θ
∘

13) Prove the following identities.   tan θ

=
sin θsin(90 −θ)

∘
 
2 2
1−tan  θ 2sin (90 − θ)−1

14) Prove the following identities.   1

−
1
=
1
−
1
 
cosec θ−cot θ sin θ sin θ cosec θ+cot θ
2 2

15) a) Prove the following identities.  

cot θ+sec  θ

2 2
= (sin θ cos θ)(tan θ + cotθ)
tan  θ+cosec  θ

(OR)
b) Prove the following identities.  tan θ
+
cot θ
= 1 + sec θ cosec θ
1−cot θ 1−tan θ

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