Class 10 Trigonometry Formula || trigonometry formula for class 10th

Class 10 Trigonometry Formula :

Table of Contents

Reciprocal Identities of Trigonometry ;

Here are the some reciprocal identities of trigonometry ,

sin θ = 1/cosec θ
cos θ = 1/sec θ
tan θ = 1/cot θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ

Pythagorean Identities of Trigonometry ;

It is based on Pythagoras theorem. This is a theorem based on the right angle trial in which the square of the hypotenuse is equal to the sum of the square of the perpendicular and the square of the base.

sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ

Co-function Identities (in Degrees) ;

The co-function or periodic identities can also be represented in degrees as:

sin(90°−x) = cos x
cos(90°−x) = sin x
tan(90°−x) = cot x
cot(90°−x) = tan x
sec(90°−x) = cosec x
cosec(90°−x) = sec x

Trigonometry Basic Formula ;

This is the basic formula of trigonometry , here are the list of this

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

Sum & Difference Identities;

here are the four sum and difference indentities formula of trigonometry ,

sin(a+b)=sin(a)cos(b)+cos(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)
cos(a-b)=cos(a)cos(b)+sin(a)sin(b)

Product to Sum Formulas;

sin a sin b = 1/2 [cos (a-b) – cos (a+b)]
cos a cos b = 1/2 [cos (a+b) + cos (a-b)]
sin a cos b = 1/2 [sin (a+b) + sin (a-b)]
cos a sin b = 1/2 [sin (a+b) – sin (a-b)]

Double Angle Formulas;

sin (2θ) = 2sinθ cosθ = 2tanθ/1+tan²θ
cos (2θ) = cos²θ – sin²θ = 2cos²θ – 1 = 1 – 2sin²θ
tan2θ = 2 tanθ / 1-tan²θ