WORKSHEET- FUNCTIONS
1. Find the domain and range of the following functions
f (x) = 2x2 – 1 and g (x) = 1 – 3x .
2. Find the domain of each of the following functions.
𝒙
(i) 𝒇(𝒙) = 𝒙𝟐 +𝟑𝒙+𝟐 (ii) f (x) = [x] + x
3. Redefine the function which is given by f (x) = |𝒙 − 𝟏| + |𝒙 + 𝟏|, – 2 ≤ x ≤ 2
4. Find the domain and range of the following functions given by
|𝒙−𝟒| 𝟏
(i) f(x) = 𝒙−𝟒 (ii) f(x) = √𝟏𝟔 − 𝒙𝟐 (iii) f(x) =
√𝟏𝟔−𝒙𝟐
𝟏
(iv) f(x) = √𝒙𝟐 − 𝟏𝟔 (v) f(x) =
√𝒙𝟐 −𝟏𝟔
𝟏
5. Find the domain of the function f given by f (x) = .
√[𝒙]𝟐 −[𝒙]−𝟔
𝟏
6. Find the domain of the function f given by f (x) = .
√𝒙 − |𝒙|
𝒙−𝟏
7. If f (x) = 𝒙+𝟏 , then show that (i) f(1/x) = - f(x) (ii) f(-1/x) = -1/f(x).
𝟏
8. Find the domain of the function f defined by f (x) = √𝟒 − 𝒙 + .
√ 𝒙𝟐 −𝟏
WORKSHEET- TRIGONOMETRY:
1. In ∆𝐴𝐵𝐶with C=90° Find the quadratic equation whose roots are tan 𝐴 and tan 𝐵
2. If sin 𝜃- 𝑠𝑖𝑛𝜑 =a, cos𝜃 + 𝑐𝑜𝑠𝜑 =b then find cos (𝜃 − 𝜑)
3. Find the number of solutions of the equation
tan 𝜃 + tan 2𝜃+tan 3𝜃 = tan 𝜃 tan 2𝜃 tan 3𝜃 in the interval of (0,𝜋)
𝟏
4. Prove that : Sin A. sin (60–A) sin (60+A) = 𝟒 Sin 3A.
5. Prove that :
𝝅
Cot 𝟐𝟒 = √2 + √3 + √4 + √6
6. If 𝛼 and 𝛽 are two different roots of the equation a cosθ+bsinθ = C.
𝟐𝒂𝒃 𝟐𝒃
Prove that (𝒂) 𝐬𝐢𝐧(𝜶 + 𝜷) = 𝒂𝟐 +𝒃𝟐 (𝒃)𝐭𝐚𝐧𝛂 + 𝐭𝐚𝐧 𝛃 = 𝒂+𝒄
7. If θ is divided into two parts such that tangent of one is k times the tangent of other and 𝜑 is their
𝒌+𝟏
difference then show that sinθ = 𝒌−𝟏 𝐬𝐢𝐧 ∅
8. A circular wire of radius 3 cm is cut and bent so as to lie along the circumference of a hoop whose
radius is 48 cm. Find the angle in degrees which is subtended at the centre of hoop.
9. Find the value of √𝟑 cosec 20° – sec 20°.
10. Find the value of tan 9° – tan 27° – tan 63° + tan 81°
𝑺𝒆𝒄 𝟖𝜽−𝟏 𝐭𝐚𝐧 𝟖𝜽
11. Prove that = .
𝑺𝒆𝒄 𝟒𝜽−𝟏 𝐭𝐚𝐧 𝟐𝜽
𝝅 𝟑𝝅 𝟓𝝅 𝟕𝝅
12. Find the value of (𝟏 + 𝐜𝐨𝐬( 𝟖 )) (𝟏 + 𝐜𝐨𝐬( ))(𝟏 + 𝐜𝐨𝐬( ))(𝟏 + 𝐜𝐨𝐬( )).
𝟖 𝟖 𝟖
𝟐𝝅 𝟒𝝅
13. If x cos θ = y cos (θ + 𝟑
) = z cos ( θ + 𝟑
), then find the value of xy + yz + zx.
14. If angle θ is divided into two parts such that the tangent of one part is k times the
𝒌+𝟏
tangent of other, and φ is their difference, then show that sin θ = 𝒌−𝟏 sin φ
15. Show that 2 sin2 β + 4 cos (α + β) sin α sin β + cos 2 (α + β) = cos 2α
16. If α and β are the solutions of the equation a tan θ + b sec θ = c, then show that
𝟐𝒂𝒄
tan (α + β) = .
𝒂𝟐 −𝒄𝟐
17. Find the smallest & greatest value of sin x cos x.
18. Prove that: sin 20° sin 40° sin 60° sin 80° = 3/16 .
𝝅 𝟐𝝅 𝟒𝝅 𝟖𝝅
19. Prove that: cos 𝟓 cos cos cos = 1/16.
𝟓 𝟓 𝟓
20. Find the value of sin 180, cos 180, sin 360 & cos 360 .
𝐭𝐚𝐧 𝟑𝒙 𝟏
21. Prove that never lies between 𝟑 and 3.
𝐭𝐚𝐧 𝒙
22. Prove that : Cos 5A = 𝟏𝟔𝑪𝒐𝒔𝟓 𝑨 − 𝟐𝟎𝑪𝒐𝒔𝟑 𝑨 + 𝟓 𝑪𝒐𝒔 𝑨
𝟏𝟎
23. Prove that : tan 𝟖𝟐 = √𝟐 + √𝟑 + √𝟒 + √𝟔.
𝟐
𝐬𝐢𝐧 𝒙 𝐬𝐢𝐧 𝟑𝒙 𝐬𝐢𝐧 𝟗𝒙 𝟏
24. Prove that : 𝐜𝐨𝐬 𝟑𝒙 + 𝐜𝐨𝐬 𝟗𝒙 + 𝐜𝐨𝐬 𝟐𝟕𝒙 = (𝐭𝐚𝐧 𝟐𝟕𝒙 − 𝐭𝐚𝐧 𝒙)
𝟐
𝝅
25. Show that : √𝟐 + √𝟐 + √𝟐 + 𝟐𝑪𝑶𝑺 𝟖𝜽 = 𝟐𝑪𝒐𝒔 𝜽, 𝟎 < 𝜽 < 𝟖
26. Prove that : 𝒕𝒂𝒏𝟕𝟎𝟎 = 𝐭𝐚𝐧 𝟐𝟎𝟎 + 𝟐 𝐭𝐚𝐧 𝟓𝟎𝟎 .
