welq t D”PZi MwYZ---Aóg Aa¨vq GmGmwm cÖ¯‘wZ cixÿv- 2023 welq †KvW t 1 2 6

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5
tan  =
12
sec
sin cos
 sin( ) + cos( ) 34
sin =
sec () + tan( ) 39

xsin + y2cos
2| X = a  bcosec a  b  0, A =
x2sin  ycos
B = 2(sincos + 3)  ( 3cos + 4sin)

X=0 tan
xcos  ysin = 0 A
B=0  0    2

tan + sec = X
sec  tan
x2 + 1
cosec =
x2  1
x= 3 0    180 

৪। cot + cosec = 3 cot2 + cosec2 = 3

cosec  cot
cos
0    2 

20 30 150
200 7
30 7
welq t D”PZi MwYZ---Aóg Aa¨vq GmGmwm cÖ¯‘wZ cixÿv- 2023 welq †KvW t 1 2 6
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20 30
204
30

720

6440 55

10 30

400

6440 5636
0.82
5636

cot + cosec = a
cosec  cot
a2  1
cos = a2 + 1

(a2 + 1) cos + (a2 + 1) sin = (a + 1)2  2

 welq t D”PZi MwYZ---Aóg Aa¨vq GmGmwm cÖ¯‘wZ cixÿv- 2023 welq †KvW t 1 2 6
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A
1 3
B D

ABCD
sin (B  D) = sin B cos D  cos B sin D
tan B + sec B  1 1 + cos D
tan B  sec B + 1 sin D

2| ABC x, y r 

sec2  tan2 = 1
cosec2  cot2 = 1

 
A= B=6
3
sin (A + B) sin (A  B)
2 tanB
tan 2B =
1  tan2 B
(i) cos (A + B) + cos (A  B) = 2 cosA cosB
ii) cos (A  B)  cos (A + B) = 2sinA sinB

 
4| A = 3 B=
6
cos (A + B) cos (A  B)
(i) cos (A + B) = cosA cosB  sin A sinB
(ii) cos (A  B) = cosA cosB + sin A sin B
(i) sin (A + B) = sinA cosB + cosA sinB
sin2 (A + B)
(ii) = tan (A  B)
3

5
 cos tan
12
cot
cos
sin + cos() 51
=
sec() + tan 26
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tan + sec = x
sec  tan
2
x 1
sin = 2
x +1
2
x 1
sin = 2 tan
x +1

tan + sin = m tan  sin = n

tan2  sin2 =
m2  n2 = 4 mn
16mn
(m + n)2 =
(m  n)2

5 , 3
sinA = cosB = 6sin2B + 5cosB = 7
13 5
cosA sinB
cotB  cotA
cotAcotB + 1
1
cotB = 
3

a
cosecA = A a>b>0
b
sinA + cosecA
b
tanA =
a  b2
2

3
a = 13 b=5 tanA + secA = 2

1 + sin
tan + sec =
1  sin
 = 45
-
tan + sec = x sin x
 welq t D”PZi MwYZ---Aóg Aa¨vq GmGmwm cÖ¯‘wZ cixÿv- 2023 welq †KvW t 1 2 6
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sec   tan  = p
sec  + tan
1  p2
sin  = 1 + p2

(1 + p2) cos  + (1 + p2) sin  + 2p2 = (1 + p)2

asin = bcos
sin + cos
sin  cos
a
cos = 
a + b2
2

a2 b2
cosec2  sec2 = b2  a2

x  3 5 7
tan + sec = A= ,B= ,C= ,D=
y 8 8 8 8
1 + sin x
=y
cos
(x2 + y2) sin = x2  y2
cos2A + cos2B + cos2C + cos2D = 2

tan + sin = m tan  sin = n

m+n
tan = 2
2 2
m  n = 4 mn
sec = mn cosec2

5| tan + sec = x
23
tan  6 
 
x2 + 1
cosec =
x2  1
(x2 + 1) cos + (x2 + 1) sin = (x + 1)2  2
 welq t D”PZi MwYZ---Aóg Aa¨vq GmGmwm cÖ¯‘wZ cixÿv- 2023 welq †KvW t 1 2 6
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1| tan + sec = x
sec  tan
x2  1
sin = x2 + 1

x2  1
sin = x2 + 1 tan

p = tan, q = sec, r = sin + cos

a asin  bcos
p = b (a  b)
a sin + bcos
y2  1
p+q=y sin = y2 + 1
r=1 sin  cos =  1

AB = 3 BC = 4
A


C
B

sin + cos 7
=
sec + tan 10
sin(A + B) + sin(B + C) + sin(C + A) = sinA + sinB + sinC

P(x,y)
r
y


O x X
M
x=y r = 2x.
sec2  tan2 = 1.
2y2 3x 
2 2  =0  0 <  < 2 ).
x +y x2 + y2

1
cosec  cot = ; 
2
cosec + cot
x2 + 1
sec = 2
x 1
2
2x x 1
1 + x2 + x2 + 1 = 2 