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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

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]

### 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

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