Trigonometric Functions: Test 4 :DPP: Chapter 3 : class 12th

Chapter 3# : Trigonometric Functions

Subject : Maths                                                         Class XII

Total Marks : 20                                                Time : 40 Min

Q1 In ΔABC if a= 13,b = 14, c =15, find the values of following    (8M)

a) cosB b) sin A/2 c) A( ΔABC) d) sin A 

Q2 In ΔABC prove that 
cotA/2 + cotB/2 + cotC/2 = (a+b+c)/(b+c-a) cotA/2                         (4M)

Q3 In ΔABC, if  Sin²A + Sin²B = Sin²C, then  show that the triangle is right angled triangle.                                                                          (4M)

Q4 Show that in ΔABC ,b cos²C/2 + c cos²B/2 = s                           (4M)

Trigonometric Functions:Test 3:DPP:Class 12th: Chapter3

Chapter 3# : Trigonometric Functions

Subject : Maths                                                         Class XII

Total Marks: 20                                                Time : 40 Min

Q 1 Find the Principal Solutions of following equation      (6M)

a) tan x = -1  
b) ⎷2.cos x + 1 = 0 
c) ⎷3.sec x + 2= 0 
d) cosec x = 2

Q2 Find the general Solution of equation(any three)        (6M)

a) sin 3x/2 = 0

b) cos (x+π/10) = 0

c) tan 2x/3 = ⎷3

d) ⎷3cosec x = 2

Q3 Find the general Solution of equation(any two)           (8M)

a) sinx . tanx = tan x - sinx+1

b) cos x + sin x = 1

c) cot x + tan x = 2 cosec x

Trigonometric functions : 12th class : TEST2 :DPP:Chapter 03

Chapter 3# : Trigonometric Functions

Subject : Maths                                                         Class XII

Total Marks: 20                                                Time : 40 Min

Q 1 Answer the following questions                                       (5M)

a) The solutions of a trigonometric equation which are not generalized by using its periodicity are known as _____.

i) General Solution  ii) Principle Solution iii) Normal Solution iv) Ordinary Solution

b) Which of the following is not a trigonometric equation.

i) sinx = ⎷3/2      ii) secӨ = cosec x   iii) ⎷3/x = 17  iv)  cosx + Sin 3x + tan 5x = 0

c) 1 - Cos²Ө = ____________

i) sec²Ө   ii) cosec²Ө  iii) tan²Ө  iv) sin²Ө

d) If cos Ө = 0 then Ө = _______

i) nπ ii) (2n+1)π/2   iii) 2nπ  iv) (2n+1)π

e) For Cos x = ½ then the general solution of x is

i) 0  ii) π/6,5π/6  iii) π/6,5π/6,13π/6….. iv) (n+1) π/6

Q2 Prove the following equations (any three)                     (6M)

a) If tan ²x =  tan ²β then x = nπ 士 β

b) Find the Principle solution of cos3x = cos2x

c) Find the general Solution of tan 3x = -1

d) Find the general solution of ⎷3cosec x = 2

Q3 Find the general Solution of equation                            (9M)

a) cos5x = sin3x

b) cosx - sinx = 1

c) 2tanx - cotx + 1 = 0