**Trigonometrical function:**In trigonometry there is importance of all thing whether it is line, angle, identities or function. Trigonometrical function has some perticular importance. If you are familiar with these function and formulas; you can easily solve problem.

So, here, we gathered all trigonometrical function and formulas. This has been done for the easiness of students or math lover. Hope, you'll like it and suggest others to at least read once.

**Reciprocal identities**

Sin x = 1/cosec x
cos x = 1/sec x tαn
x = 1/ cot x

cosec x = 1/sin x
sec = 1/cos x cot x = 1/tαn x

**Pythagorean Identities**

sin

^{2}x + cos^{2}x = 1
1 + tαn

1 + cot^{2}x = sec^{2}x^{2}x = cosec

^{2}x

**Quotient Identities**

tαn x = sin x/ cos x,

cot x = cos x/ sin x

**Co-Function Identities**

sin (π/2
– x) = cos x

cos (π/2
– x) = sin x

tαn (π/2
– x) = cot x

cosec (π/2
– x) = sec x

sec(π/2
– x) = cosec x

cot (π/2
– x) = tαn x

**Even – Odd Identities**

Sin (- α)
= - sin α cos(- α) = cos α, tαn( - α ) = - tαn α

Cosec ( - α) = - cosec α, sec (- α) = sec α cot (- α) = -
cot α

**Sum – Difference formulas**

sin (x + y) = sin x cosy + cos x sin y

Cos (x + y) = cos x cox y -+ sin x sin y

tan (x + y ) = tan x + tαn y/ 1-+ tan x. tan y

**Double Αngle Formulas**

sin (2x) = 2sin x cosx

cos (2x) = cos2 x – sin 2 x

= 2cos2 x
– 1 = 1 2 sin2 x

tan (2x) = 2tan x/ 1 – tan2 x/1 tan2 x

**Power-Reducing / Half angle formulas**

Sin2 x = 1 – cos (2x)/2

Cos2 x = 1 + cos (2x)/2

tan2 x = 1 – cos (2x)/1 + cos (2x)

**Sum to Product Formulas**

Sin x + sin y = 2 sin (x + y/2) cos (x – y/2)

Sin x – sin y = 2 cos (x + y/2) sin (x – y/2)

cos x + cos y = 2 cos (x + y/2) cos (x – y/2)

cos x – cos y = – 2sin
(x + y/2) sin (x – y/2)

**Product to Sum Formulas**

sin x.sin y = ½ [cos (x – y) – cos (x + y )]

cos x cos y = ½ [cos (x – y) + cos (x + y)]

sin x cos y = ½ [sin (x +y) + sin (x – y)]

cos x cos y = ½ [sin (x – y) – sin (x – y)]