ТАКА....

sin θ = Opposite Side/Hypotenuse.
cos θ = Adjacent Side/Hypotenuse.
tan θ = Opposite Side/Adjacent Side.
sec θ = Hypotenuse/Adjacent Side.
cosec θ = Hypotenuse/Opposite Side.
cot θ = Adjacent Side/Opposite Side.given.
cos (A + B) = cos A cos B – sin A sin B.
cos (A – B) = cos A cos B + sin A sin B.
sin (A+B) = sin A cos B + cos A sin B.
sin (A -B) = sin A cos B – cos A sin B.
If sin 𝜃 = –4/5 and 𝜋 < 𝜃 < 3𝜋/2, find the value of all the other five trigonometric functions.
sin (-θ) = − sin θ
cos (−θ) = cos θ
tan (−θ) = − tan θ
cosec (−θ) = − cosec θ
sec (−θ) = sec θ
cot (−θ) = − cot θ
Sin θ = Opposite side of angle θ/Hypotenuse.
Cos θ = Adjacent side of angle θ/Hypotenuse.
Tan θ = Opposite side of angle θ/Adjacent side of angle θ
Sec θ = Hypotenuse/Adjacent side of angle θ
Cosec θ = Hypotenuse/Opposite side of angle θ

Product to Sum Formulas

sin x sin y = 1/2
cos x cos y = 1/2
sin x cos y = 1/2[sin(x+y) + sin(x−y)]
cos x sin y = 1/2[sin(x+y) – sin(x−y)]
Sum to Product Formulas
sin x + sin y = 2 sin
sin x – sin y = 2 cos
cos x + cos y = 2 cos
cos x – cos y = -2 sin

Identities

sin2 A + cos2 A = 1
1+tan2 A = sec2 A
1+cot2 A = cosec2 A
sin(π/2-A) = cos A
cos(π/2-A) = sin A
sin(π-A) = sin A
cos(π-A) = -cos A
sin(π+A)=-sin A
cos(π+A)=-cos A
sin(2π-A) = -sin A
cos(2π-A) = cos A
tan(A+B) = [(tan A + tan B)/(1 – tan A tan B)]
tan(A-B) = [(tan A – tan B)/(1 + tan A tan B)]
cot(A+B) = [(cot A cot B − 1)/(cot B + cot A)]
cot(A-B) = [(cot A cot B + 1)/(cot B – cot A)]

Some additional formulas for sum and product of angles:

cos(A+B) cos(A–B)=cos2A–sin2B=cos2B–sin2A
sin(A+B) sin(A–B) = sin2A–sin2B=cos2B–cos2A
sinA+sinB = 2 sin (A+B)/2 cos (A-B)/2

Formulas for twice of the angles:

sin2A = 2sinA cosA = [2tan A /(1+tan2A)]
cos2A = cos2A–sin2A = 1–2sin2A = 2cos2A–1= [(1-tan2A)/(1+tan2A)]
tan 2A = (2 tan A)/(1-tan2A)

Formulas for thrice of the angles:

sin3A = 3sinA – 4sin3A
cos3A = 4cos3A – 3cosA
tan3A = [3tanA–tan3A]/[1−3tan2A]