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Trigonometry All Formula
No.-1. Reciprocal Identities
The Reciprocal Identities are given as:
No.-1. cosec θ = 1/sin θ
No.-2. sec θ = 1/cos θ
No.-3. cot θ = 1/tan θ
No.-4. sin θ = 1/cosec θ
No.-5. cos θ = 1/sec θ
No.-6. tan θ = 1/cot θ
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No.-6. Last One Year Current Affairs PDF Download
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Periodicity Identities (in Radians)
These formulas are used to shift the angles by π/2, π, 2π, etc. They are also called cofunction identities.
No.-1. sin (π/2 – A) = cos A & cos (π/2 – A) = sin A
No.-2. sin (π/2 + A) = cos A & cos (π/2 + A) = – sin A
No.-3. sin (3π/2 – A) = – cos A & cos (3π/2 – A) = – sin A
No.-4. sin (3π/2 + A) = – cos A & cos (3π/2 + A) = sin A
No.-5. sin (π – A) = sin A & cos (π – A) = – cos A
No.-6. sin (π + A) = – sin A & cos (π + A) = – cos A
No.-7. sin (2π – A) = – sin A & cos (2π – A) = cos A
No.-8. sin (2π + A) = sin A & cos (2π + A) = cos A
Cofunction Identities (in Degrees)
The cofunction or periodic identities can also be represented in degrees as:
No.-1. sin(90°−x) = cos x
No.-2. cos(90°−x) = sin x
No.-3. tan(90°−x) = cot x
No.-4. cot(90°−x) = tan x
No.-5. sec(90°−x) = cos x
No.-6. cec(90°−x) = sec x
Sum & Difference Identities
No.-1. sin(x+y) = sin(x)cos(y)+cos(x)sin(y)
No.-2. cos(x+y) = cos(x)cos(y)–sin(x)sin(y)
No.-3. tan(x+y) = (tan x + tan y)/ (1−tan x •tan y)
No.-4. sin(x–y) = sin(x)cos(y)–cos(x)sin(y)
No.-5. cos(x–y) = cos(x)cos(y) + sin(x)sin(y)
No.-6. tan(x−y) = (tan x–tan y)/ (1+tan x • tan y)
Double Angle Identities
No.-1. sin(2x) = 2sin(x) • cos(x) = [2tan x/(1+tan2 x)]
No.-2. cos(2x) = cos2(x)–sin2(x) = [(1-tan2 x)/(1+tan2 x)]
No.-3. cos(2x) = 2cos2(x)−1 = 1–2sin2(x)
No.-4. tan(2x) = [2tan(x)]/ [1−tan2(x)]
No.-5. sec (2x) = sec2 x/(2-sec2 x)
No.-6. csc (2x) = (sec x. csc x)/2
Triple Angle Identities
No.-1. Sin 3x = 3sin x – 4sin3x
No.-2. Cos 3x = 4cos3x-3cos x
No.-3. Tan 3x = [3tanx-tan3x]/[1-3tan2x]
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No.-5. Exam Wise Complete PDF Notes According Syllabus
No.-6. Last One Year Current Affairs PDF Download
No.-7. Join Our Whatsapp Group
No.-8. Join Our Telegram Group
Important MCQ’s
Que.-1.’फैजी’ किसके दरबार में रहते थे?
(a) औरंगजेब
(b) अकबर
(c) जहाँगीर
(d) शाहजहाँ
Ans (b) अकबर
Que.-2.चारमीनार कहाँ स्थित है?
(a) आगरा
(b) उदयपुर
(c) हैदराबाद
(d) चंडीगढ़
Ans (c) हैदराबाद