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. I. sin θ = Perpendicular/Hypotenuse
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Cosecant, secant, और cotangent मूल त्रिकोणमितीय अनुपात साइन, कोसाइन और स्पर्शरे खा
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आवर्त सर्वसमिकाओं वाले त्रिकोणमिति सूत्रों का उपयोग कोणों को π/2, , 2π, आदि से स्थानांतरित MTS Exam with short tricks | PDF
करने के लिए किया जाता है। सभी त्रिकोणमितीय सर्वसमिकाएँ प्रकृ ति में चक्रीय होती हैं, जिसका अर्थ  Download pdf notes  May 15, 2022

है कि वे एक अवधि के बाद स्वयं को दोहराते हैं।

आवर्त सर्वसमिकाओं पर विभिन्न त्रिकोणमिति सूत्रों के लिए यह अवधि भिन्न होती है। उदाहरण के TOPICS
लिए, tan 30° = tan 210° लेकिन यह cos 30° और cos 210° के लिए सही नहीं है। आप ज्या और
कोज्या फलनों की आवधिकता को सत्यापित करने के लिए नीचे दिए गए त्रिकोणमिति सूत्रों का उल्लेख BOOKS (153) PAPER (97) GK (84)

कर सकते हैं। SYLLABUS (84) TEACHERS (65) TET (53)

First Quadrant: UP (47) NEWS (38) AIRFORCE (32)

COAST GUARD (31) UP TET (30) NAVY (28)

. I. sin (π/2 – θ) = cos θ
POLICE (27) ENGLISH PDF NOTES (26)
. II. cos (π/2 – θ) = sin θ
MATH (26) STATIC GK (25) CTET (23)
. III. sin (π/2 + θ) = cos θ
PRACTICE SETS (23) SSC (22) SCIENCE (22)
. IV. cos (π/2 + θ) = – sin θ
MOCK TEST (20) SUPER TET (19)
Second Quadrant:
HISTORY (15) ARMY (14) UPSC (14)
 I. sin (3π/2 – θ) = – cos θ COMPUTER (13) RAJASTHAN (13)
 II. cos (3π/2 – θ) = – sin θ HINDI (12) GEOGRAPHY (12) UPSSSC (10)
 III. sin (3π/2 + θ) = – cos θ
STATE GK (9) RAILWAY (9) IAS (8)
 IV. cos (3π/2 + θ) = sin θ
NEET (8) REASONING (8) MTS (7)

Third Quadrant: PET (7) BIOLOGY (7) NDA (6)

 I. sin (π – θ) = sin θ PHYSICS (6) AGNEEPATH (5) REET (5)

 II. cos (π – θ) = – cos θ MP (5) UPBOARD (5) TECH (4)

 III. sin (π + θ) = – sin θ CHEMISTRY (4) COURT (4) UP GK (4)

 IV. cos (π + θ) = – cos θ POLITY (3) UTTARAKHAND (3) CLERK (3)

HARYANA (3) HSSC (3) MP BOARD (2)

Fourth Quadrant:
POLYTECHNIC (2) EXAM PATTERN (2)
 I. sin (2π – θ) = – sin θ
SANSKRIT (2) SSB (2) IIT JEE (1)
 II. cos (2π – θ) = cos θ
TELANGANA (1)
 III. sin (2π + θ) = sin θ
 IV. cos (2π + θ) = cos θ

TRIGONOMETRY FORMULAS INVOLVING CO-FUNCTION IDENTITIES(IN DEGREES)

सह-कार्य पहचान पर त्रिकोणमिति सूत्र विभिन्न त्रिकोणमिति कार्यों के बीच अंतर्संबंध प्रदान करते हैं। सह-कार्य
त्रिकोणमिति सूत्र नीचे डिग्री में दर्शाए गए हैं :

 I. sin(90° − x) = cos x
 II. cos(90° − x) = sin x
 III. tan(90° − x) = cot x
 IV. cot(90° − x) = tan x
 V. sec(90° − x) = cosec x

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 VI. cosec(90° − x) = sec x

TRIGONOMETRY FORMULAS INVOLVING SUM AND DIFFERENCE IDENTITIES

योग और अंतर पहचान में sin(x + y), cos(x - y), cot(x + y), आदि के त्रिकोणमिति सूत्र शामिल हैं।

 I. sin(x + y) = sin(x)cos(y) + cos(x)sin(y)

 II. cos(x + y) = cos(x)cos(y) - sin(x)sin(y)
 III. tan(x + y) = (tan x + tan y)/(1 - tan x • tan y)
 IV. sin(x – y) = sin(x)cos(y) - cos(x)sin(y)
 V. cos(x – y) = cos(x)cos(y) + sin(x)sin(y)
 VI. tan(x − y) = (tan x - tan y)/(1 + tan x • tan y)

TRIGONOMETRY FORMULAS FOR MULTIPLE AND SUB-MULTIPLE ANGLES

कई और उप-एकाधिक कोणों के लिए त्रिकोणमिति सूत्रों का उपयोग आधे कोण, दोहरे कोण, ट्रि पल
कोण आदि के लिए त्रिकोणमितीय कार्यों के मूल्य की गणना के लिए किया जा सकता है।
TRIGONOMETRY FORMULAS INVOLVING HALF-ANGLE IDENTITIES
The half of the angle x is presented through the below few trigonometry formulas.
 I. sin (x/2) = ±√[(1 - cos x)/2]
 II. cos (x/2) = ± √[(1 + cos x)/2]
 III. tan (x/2) = ±√[(1 - cos x)/(1 + cos x)] or, tan (x/2) = ±√[(1 - cos x)(1 -
cos x)/(1 + cos x)(1 - cos x)]
 IV. tan (x/2) = ±√[(1 - cos x)2/(1 - cos2x)] ⇒ tan (x/2) = (1 - cos x)/sin x

TRIGONOMETRY FORMULAS INVOLVING DOUBLE ANGLE IDENTITIES

कोण x का दोहरा नीचे कु छ त्रिकोणमिति सूत्रों के माध्यम से प्रस्तुत किया गया है।

 I. sin (2x) = 2sin(x) • cos(x) = [2tan x/(1 + tan2 x)]

 II. cos (2x) = cos2(x) - sin2(x) = [(1 - tan2 x)/(1 + tan2 x)]
 III. cos (2x) = 2cos2(x) - 1 = 1 - 2sin2(x)
 IV. tan (2x) = [2tan(x)]/ [1 - tan2(x)]
 V. sec (2x) = sec2 x/(2 - sec2 x)
 VI. cosec (2x) = (sec x • cosec x)/2

TRIGONOMETRY FORMULAS - SUM AND PRODUCT IDENTITIES

योग या उत्पाद पहचान के लिए त्रिकोणमितीय सूत्रों का उपयोग उनके उत्पाद रूप में या इसके
विपरीत किन्हीं दो त्रिकोणमितीय कार्यों के योग का प्रतिनिधित्व करने के लिए किया जाता है।
TRIGONOMETRY FORMULAS INVOLVING PRODUCT IDENTITIES
 I. sinx⋅cosy = [sin(x + y) + sin(x − y)]/2
 II. cosx⋅cosy = [cos(x + y) + cos(x − y)]/2
 III. sinx⋅siny = [cos(x − y) − cos(x + y)]/2

TRIGONOMETRY FORMULAS INVOLVING SUM TO PRODUCT IDENTITIES

दो न्यून कोणों A और B के संयोजन को नीचे दिए गए त्रिकोणमिति सूत्रों में त्रिकोणमितीय अनुपातों के
माध्यम से प्रस्तुत किया जा सकता है।
 I. sinx + siny = 2[sin((x + y)/2)cos((x − y)/2)]
 II. sinx − siny = 2[cos((x + y)/2)sin((x − y)/2)]
 III. cosx + cosy = 2[cos((x + y)/2)cos((x − y)/2)]
 IV. cosx − cosy = −2[sin((x + y)/2)sin((x − y)/2)]

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TRIGONOMETRY FORMULAS INVOLVING TRIPLE ANGLE IDENTITIES

कोण x का त्रिगुण नीचे कु छ त्रिकोणमिति सूत्रों के माध्यम से प्रस्तुत किया गया है।
 I. sin 3x = 3sin x - 4sin3x
 II. cos 3x = 4cos3x - 3cos x
 III. tan 3x = [3tanx - tan3x]/[1 - 3tan2x]

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