Trigonomerical Identitiies

 Trigonomerical Identities       practice sums👈1

                                                                                                  PRACTICE SUMS👈2

Trigonometric Identities & Helpful Algebraic Identities

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🔹 Basic Trigonometric Identities

These are the core identities used to simplify and prove other trigonometric expressions.

✅ 1. Reciprocal Identities

$$\sin \theta = \frac{1}{\csc \theta},\quad \cos \theta = \frac{1}{\sec \theta},\quad \tan \theta = \frac{1}{\cot \theta}$$

✅ 2. Quotient Identities

$$\tan \theta = \frac{\sin \theta}{\cos \theta},\quad \cot \theta = \frac{\cos \theta}{\sin \theta}$$

✅ 3. Pythagorean Identities

$$\sin^2 \theta + \cos^2 \theta = 1 \\ 1 + \tan^2 \theta = \sec^2 \theta \\ 1 + \cot^2 \theta = \csc^2 \theta$$

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🔹 Algebraic Identities Helpful in Trigonometry

These are often used to simplify trigonometric expressions and prove identities.

✅ 1. Square of a Sum

$$(a + b)^2 = a^2 + 2ab + b^2$$

✅ 2. Square of a Difference

$$(a - b)^2 = a^2 - 2ab + b^2$$

✅ 3. Difference of Squares

$$a^2 - b^2 = (a + b)(a - b)$$

✅ 4. Factoring Common Terms

$$ab + ac = a(b + c)$$

.*Rationalizing

Multiply by conjugate:

$$\frac{1}{a + b} \times \frac{a - b}{a - b} = \frac{a - b}{a^2 - b^2}$$