Trigonometric Identities
ICSE · Class 10 · Mathematics
Summary of Trigonometric Identities for ICSE Class 10 Mathematics. Key concepts, important points, and chapter overview.
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Trigonometric identities are equations that remain true for all values of the angle. The chapter focuses on three fundamental identities, the reciprocal and quotient relations of trigonometric ratios, and the correct method for proving identities by transforming one side of an equation until it matc
Key Concepts
The ratios of sides of
The ratios of sides of a right triangle with respect to an acute angle are called trigonometric ratios. For angle A, sin A = BC/AC, cos A = AB/AC, and
The hypotenuse is the side opposite
The hypotenuse is the side opposite the 90 degree angle. The base is the side at which the right angle and the given angle lie. The perpendicular is t
sine A is the reciprocal
sine A is the reciprocal of cosecant A, cosine A is the reciprocal of secant A, and tangent A is the reciprocal of cotangent A. In formula form, sin θ
tan θ = sin θ /
tan θ = sin θ / cos θ and cot θ = cos θ / sin θ.
sin^2 A + cos^2 A =
sin^2 A + cos^2 A = 1, where A is an acute angle.
Learning Objectives
- Understand the meaning of trigonometric identities
- Recall the standard trigonometric ratios of sine, cosine, tangent, cosecant, secant, and cotangent
- Use reciprocal and quotient relations correctly
- Learn the three fundamental identities: sin^2 A + cos^2 A = 1, 1 + tan^2 A = sec^2 A, and 1 + cot^2 A = cosec^2 A
- Apply Pythagoras theorem to prove trigonometric identities
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