Trigonometric Identities (त्रिकोणमितीय सर्वसमिकाएं) In Hindi
त्रिकोणमितीय सर्वसमिकाएं गणितीय समीकरण हैं जो समकोण त्रिकोणों में sine, cosine, tangent, cosecant, secant और cotangent जैसे त्रिकोणमितीय अनुपातों के बीच संबंध स्थापित करती हैं। ये सर्वसमिकाएं अनेक प्रकार की होती हैं और इनका उपयोग ज्यामितीय और त्रिकोणमितीय समस्याओं को हल करने में किया जाता है।
Trigonometric Identities In English
Trigonometric identities are equations involving trigonometric functions (sine, cosine, tangent, etc.) that hold true for all allowed values of the angles involved. These identities are very useful in simplifying trigonometric expressions and solving trigonometric equations.
Trigonometric Formula
(Perpendicular)² + (Base)² = (Hypotenuse)²
- (P)² + (B)² = (H)²
Trigonometric properties
- sin A = \( \frac{P}{H} \)
- cos A = \( \frac{B}{H} \)
- tan A = \( \frac{P}{B} \)
- cot A = \( \frac{B}{P} \)
- cosec A = \( \frac{H}{P} \)
- sec A = \( \frac{H}{B} \)
Relation Between Trigonometric Identities:
- tan A = \( \frac{sin A}{cos A} \)
- cot A = \( \frac{cos A}{sin A} \)
- cosec A = \( \frac{1}{sin A} \)
- sec A = \( \frac{1}{cos A} \)
Trigonometric Identities:
- sin²A + cos²A = 1
- tan²A + 1 = sec²A
- cot²A + 1 = cosec²A
Trigonometry Negative Formulas
- sin(-θ) = – sinθ
- cos(-θ) = cosθ
- tan(-θ) = – tanθ
- cosec(-θ) = – cosecθ
- sec(-θ) = secθ
- cot(-θ) = – cotθ
Product to Sum Formulas
- sin(A) cos(B) = \( \frac{1}{2} \) [sin(A + B) + sin(A – B)]
- cos(A) sin(B) = \( \frac{1}{2} \) [sin(A + B) – sin(A – B)]
- cos(A) cos(B) = \( \frac{1}{2} \) [cos(A + B) + cos(A – B)]
- sin(A) sin(B) = \( \frac{1}{2} \) [cos(A – B) – cos(A + B)]
Sum to Product Formulas
Sine Sum-to-Product Formula:
- sin(a) + sin(b) = 2 sin (\( \frac{a+b}{2} \)) cos (\( \frac{a-b}{2} \))
- sin(a) – sin(b) = 2 cos (\( \frac{a+b}{2} \)) sin (\( \frac{a-b}{2} \))
Cosine Sum-to-Product Formula:
- cos(a) + cos(b) = 2 cos (\( \frac{a+b}{2} \)) cos (\( \frac{a-b}{2} \))
- cos(a) – cos(b) = -2 cos (\( \frac{a+b}{2} \)) sin (\( \frac{a-b}{2} \))
Leave a Reply