Trigonometric Identities Class 11

 Here are some of the most commonly used trigonometric identities:

Pythagorean Identity:

cos²(θ) + sin²(θ) = 1

1+tan²(θ)  = sec²(θ)

cosec²(θ) = 1 + cot²(θ)

Reciprocal Identities:

cosec(θ) = 1/sin(θ)

sec(θ) = 1/cos(θ)

cot(θ) = 1/tan(θ)

Quotient Identities:

tan(θ) = sin(θ)/cos(θ)

cot(θ) = cos(θ)/sin(θ)

Complementary Function Identities:

sin(90° - θ) = cos(θ)

cos(90° - θ) = sin(θ)

tan(90° - θ) = cot(θ)

cot(90° - θ) = tan(θ)

Odd-Even Identities:

sin(-θ) = -sin(θ)

cos(-θ) = cos(θ)

tan(-θ) = -tan(θ)

Double Angle Identities:

sin(2θ) = 2sin(θ)cos(θ)

cos(2θ) = cos^2(θ) - sin^2(θ)

tan(2θ) = 2tan(θ)/(1-tan^2(θ))

Half Angle Identities:

sin(θ/2) = ±√[(1-cos(θ))/2]

cos(θ/2) = ±√[(1+cos(θ))/2]

tan(θ/2) = ±√[(1-cos(θ))/(1+cos(θ))]

These are some of the most commonly used trigonometric identities. It is important to note that there are many more identities, and these are just a few examples to get you started.