Скачать или смотреть Trigonometry class 10 ,chapter 8, exercise 8.2 Question : 1(i,ii,iii,iv,v)part

🔷 Basic Trigonometric Ratios

In a right-angled triangle (angle θ):

sin θ = Opposite / Hypotenuse

cos θ = Adjacent / Hypotenuse

tan θ = Opposite / Adjacent

Other derived ratios:

cosec θ = 1 / sin θ

sec θ = 1 / cos θ

cot θ = 1 / tan θ

🔷 Trigonometric Identities

Pythagorean Identities

sin²θ + cos²θ = 1

1 + tan²θ = sec²θ

1 + cot²θ = cosec²θ

Reciprocal Identities

sin θ = 1 / cosec θ

cos θ = 1 / sec θ

tan θ = 1 / cot θ

Quotient Identities

tan θ = sin θ / cos θ

cot θ = cos θ / sin θ

🔷 Trigonometric Values of Standard Angles

θ (Angle)sin θcos θtan θ0°01030°1/2√3/21/√345°√2/2√2/2160°√3/21/2√390°10Undefined

🔷 Co-Function Identities

sin(90° − θ) = cos θ

cos(90° − θ) = sin θ

tan(90° − θ) = cot θ

cot(90° − θ) = tan θ

sec(90° − θ) = cosec θ

cosec(90° − θ) = sec θ

🔷 Angle Sum and Difference Formulas

sin(A ± B) = sin A cos B ± cos A sin B

cos(A ± B) = cos A cos B ∓ sin A sin B

tan(A ± B) = (tan A ± tan B) / (1 ∓ tan A tan B)

🔷 Double Angle Formulas

sin(2θ) = 2 sin θ cos θ

cos(2θ) = cos²θ − sin²θ = 2 cos²θ − 1 = 1 − 2 sin²θ

tan(2θ) = 2 tan θ / (1 − tan²θ)

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