Model Question Paper

Trigonometry - Part II
10th Standard

Maths Reg.No. :            

I.Answer all the questions.

II.Use blue pen only.
Time : 01:00:00 Hrs Total Marks : 40
Part-A 5x1=5
1) 4
cos x − sin x =
4

(a) 2sin x − 1
2
(b) 2
2cos x − 1 (c) 1 + 2sin x
2
(d) 1 − 2cos x
2

2) If tanθ = a

x
,  then the value of  x
=
√a 2 +x2

(a) cosθ (b) sinθ (c) cosecθ (d) secθ

3) If x = a
2 y
 then the value of  x
secθ, y = b tanθ, − =
2 2
a x

(a) 1 (b) -1 (c) tan θ

2
(d) cosec θ
2

4) secθ
=
cotθ+tanθ

(a) cotθ (b) tanθ (c) sinθ (d) −cotθ

∘ ∘

5) sin(90 −θ)sinθ cos(90 −θ)cosθ

+ =
tanθ cotθ

(a) tanθ (b) 1 (c) -1 (d) sinθ

Part-B 5 x 2 = 10
6) Determine whether each of the following is an identity or not cos 2 2
θ  +  sec  θ = 2 + sin θ  
7) Prove the following identities  sec 2 2
 θ + cosec θ = sec  θ cosec  θ
2 2

8) A kite is flying with a string of length 200 m. If the thread makes an angle 30  with the ground, find the distance of the kite from the ground level. (Here, assume that the string is
∘

along a straight line)

9) A ladder leaning against a vertical wall, makes an angle of 60 with the ground. The foot of the ladder is 3.5 m away from the wall. Find the length of the ladder.
∘

10) Find the angular elevation (angle of elevation from the ground level) of the Sun when the length of the shadow of a 30 m long pole is 10√−−
−
3m .

Part-C 5 x 5 = 25
11) If tan θ + sin θ = m, tanθ − sin θ = m  and m ≠ n then show that m 2
−n
2 −
−
= 4√mn
−

12) If tan 2
α = cos β − sin β
2 2
 then prove that cos 2
α − sin α = tan β
2 2

13) Prove the following identities.    sin(90 − θ)

+
cos θ
∘
= 2sec θ   
1+sin θ 1−cos(90 − θ)

14) If x = a secθ + b tan θ and y = a tan θ + b sec θ, then prove that x 2

−y
2
= a
2
−b
2

15) If tan θ = n tan α  and sin θ = m sin α then prove that cos 2

 θ =
m −1

2
, n ≠ ±1
n −1

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