1) sec 11/cosec 79. 1
2) sin 20°30'/cos 69° 30'. 1
3) (sin 49/cos 41)² +(cos 41/sin 49)² . 1
4) (tan 20/cosec 70)² +(cot 20/sec 70)² . 1
5) (cot 40/tan 50) +1/2 (cos 35/sin 55). 1/2
6) cosec²67 - tan²23. 1
7) (sin 72/cos 18) +(sin 72- cos 18) . 0
8) (sin 35 sin 55) - (cos 35 cos 55) . 0
9) sin² 20 + sin² 70 - tan² 45. 0
10) sec 50 sin 40 + cos 40 cosec 50. 2
B) Express each one of the following in terms of Trigonometric ratios of angles lying between 0 and 45:::
1) sin 59 + cos 56. Cos 31+sin34
2) tan 65+ cot 49. Cot 25+ tan 41
3) cos 78+ sec 78. sin 12+ cosec 12
C) If A and B are angles of a right angled triangle ABC, right angled at C, prove that
1) sin² A+ sin²B = 1
2) 1 + tan²A= cosec²B.
3) 1+ cot²A= sec² B
D) If A, B, C are the interior angles of a triangle ABC , prove that tan(A+C)/2= cot B/2
E) PROVE:
1) tan 20 tan35 tan45 tan55 tan 70= 1
2) Sin 48 sec42 + cos48 cosec 42 =2
3) Sin 63 cos27 + cos63 sin 27 =1
4) Sin 70/cos20 + cosec20/sec70 - 2 cos70 cosec 20 =0
5) cos80/ sin10 + cos59 cosec31 =2
6) Sinx sin(90-x)- cosx cos(90-x) =0
7) {Sinx cos(90-x) cosx}/sin(90-x) + {cosx sin(90-x) sinx}/cos(90-x) =1
8) Sinx/sin(90-x) + cosx/cos(90-x) = secx Cosecx.
9) sin(90-x) cos(90-x) =tanx/{1+ cot²(90-x)}
10) cos(90-x)/(1+ sin(90-x) + (1+ sin(90-x)/cos(90-x) = 2 Cosecx
11) 1/(1+ cos(90-x) + 1/(1- cos(90-x) = 2 cosec²(90-x)
12) sin²(90-x)(1+ cot²(90-x)) =1
13) {cos(90-x) sec(90-x) tanx}/{ cosec(90-x) sin(90-x) cot(90-x)} + tan(90-x)/cotx=2
14){ tan(90-x) cotx}/cosec²x - cos²x = 0
15) {cos(90-x) sin(90-x)/tan(90-x) = sin²x.
16) sec²80 - cot²80+ {sin15 cos75 + cos15 sin75}/{cosx sin(90-x)+ sinx cos(90-x) = 2
17) cotx tan(90-x)- sec(90-x) cosecx + sin²25 + sin²65 + √3(tan5 tan 45 tan85) =√3
18) Sin(50+x)- cos(40-x)+ tan1 tan 10 tan20 tan70 tan80 tan89= 1
19) cotx tan(90-x) - Sec(90-x) Cosecx +√3(tan5 tan 30 tan85)+ sin²25+ sin²65= 1
20) {- tan x cot(90-x)+ secx cosec(90-x)+ sin²35+ sin²55}/{tan 10 tan20 tan45 tan70 tan 80}=2
F) EVALUATE:
1) 2/3(cos⁴30 - sin⁴45)-3(sin²60 - sec²45)+ 1/4 cot²30. 113/24
2) 4(sin⁴30 + cos⁴60)- 2/3(sin²60 - cos²45)+ 1/2 tan²60. 11/6
3) sin50/cos40 + cosec40/ sec50 - 4 cos50 cosec 40. -2
4) (cos²20 +cos²70)/(sin²59 + sin²31) + sin35 sec 55. 2
5) tan35 tan 40 tan45 tan50 tan55. 1
6) cosec(65+x) - sec(25-x) - tan(55-x)+ cot(35+x). 0
7) tan7 tan23 tan60 tan67 tan83. √3
8) 2sin68/cos22 - 2 cot15/5 tan 75 - (3 tan45 tan20 tan 40 tan50 tan70)/5. 1
G) If A, B, C are the interior angles of∆ ABC, show that
1) sin{(A+B)/2}= cos(A/2)
2) cos{(B+C)/2}= sin(A/2)
3) cos²{(B+C)/2}+cos²(A/2)= 1
4) 1 + tan²{(B+C)/2}= cosec²(A/2)
5) tan{(B+C)/2}= cot(A/2)
H) If A and B are angles of a right angled at C, prove
1) sin²A + sin²B= 1
2) 1 + tan²A = cosec²B
3) 1 + cot²A = sec²B
I) If 2x + 45 and 30 - x are acute angles, find the degree measure of x satisfying sin(2x+45)= cos(30-x). 15°
J) if x is a positive acute angle such that secx= cosec 60, find the value of 2 cos²x -1. . 1/2
K) PROVE:
1) sec²16 - 1/(tan²74)= 1
2) sec²18 - 1/tan²72 = 1
L) If A and B are complementary angles, prove
1) (sinA + sinB)²= 1+ 2 sinA cosA
2) sin²A + sin²B= 1
3) cot B + cos B= cosB(1+sinB)/cosA
4) 1+ tanA/tanB = tan²A sec²B
5) √{tanA tanB + tanA cotB)/(sinA secB) - (sin²B/cos²A)}= tanA
M) Evaluate:
1) sin²1 + sin²3 + sin²5 + ....... sin²87+sin²89. 45/2
2) cot12 cot38 cot52 cot60 cot78. 1/√3
3) tan5 tan25tan30 tan65 tan85. 1/√3
N) if cos2x = sin 4x, where 2x and 4x are acute angles, find the value of x. 15
O) If sin3x = cos(x - 6), where 3x and x-6 are acute angles, find the value of x. 24
P) If sin(x+36)= cosx , where x+ 36 is acute angle. 27
Q) If tan2x= cot(x+6), where 2x and x+6 are acute angle, find the value of x. 28
R) If sin5x = cos4x , find x. 10
No comments:
Post a Comment