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
sin2 x + cos2 x = 1
1 + tαn2 x = sec2 x
1 + cot2 x
= cosec2 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)]
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