Human Eye #Science class 10# NCERT ch 10 CBSE#Siddhant Scholars
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Here are Class 10 / 9 Trigonometry Formulas in a clean, exam-ready (20-mark style) with headings, features, and conclusion — exactly the way you prefer.
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✦ TRIGONOMETRY FORMULAS (FULL NOTES)
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1. Basic Trigonometric Ratios (Right-Angled Triangle)
For a triangle ABC with ∠C = 90°:
sin θ = Perpendicular / Hypotenuse
cos θ = Base / Hypotenuse
tan θ = Perpendicular / Base
cot θ = Base / Perpendicular
sec θ = Hypotenuse / Base
cosec θ = Hypotenuse / Perpendicular
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2. Reciprocal Identities
sin θ = 1 / cosec θ
cos θ = 1 / sec θ
tan θ = 1 / cot θ
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3. Quotient Identities
tan θ = sin θ / cos θ
cot θ = cos θ / sin θ
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4. Pythagorean Identities
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
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5. Trigonometric Values for Standard Angles
(i) sin θ values
θ : 0°, 30°, 45°, 60°, 90°
sin : 0, 1/2, 1/√2, √3/2, 1
(ii) cos θ values
θ : 0°, 30°, 45°, 60°, 90°
cos : 1, √3/2, 1/√2, 1/2, 0
(iii) tan θ values
θ : 0°, 30°, 45°, 60°, 90°
tan : 0, 1/√3, 1, √3, ∞
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6. Trigonometric Ratios of Complementary Angles
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
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7. Trigonometric Identities (Important)
sin 2θ = 2 sin θ cos θ
cos 2θ = cos²θ – sin²θ
tan 2θ = 2 tan θ / (1 – tan²θ)
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8. Height & Distance Formulas
Used in Class 10 Applications:
tan θ = Height / Distance
cot θ = Distance / Height
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Conclusion (Exam-style)
Trigonometry mainly depends on ratios, standard angles, and identities.
If you remember:
⭐ sin–cos pair,
⭐ tan = sin/cos,
⭐ sin² + cos² = 1,
then the entire chapter becomes easy and scoring.
---
If you want, I can send:
✅ Colourful PDF Notes
✅ Full Trigonometry Formula Chart (HD)
✅ Important 50 MCQs + Answers
Just tell me “Trigonometry chart”, or “MCQ test”.
---
✦ TRIGONOMETRY FORMULAS (FULL NOTES)
---
1. Basic Trigonometric Ratios (Right-Angled Triangle)
For a triangle ABC with ∠C = 90°:
sin θ = Perpendicular / Hypotenuse
cos θ = Base / Hypotenuse
tan θ = Perpendicular / Base
cot θ = Base / Perpendicular
sec θ = Hypotenuse / Base
cosec θ = Hypotenuse / Perpendicular
---
2. Reciprocal Identities
sin θ = 1 / cosec θ
cos θ = 1 / sec θ
tan θ = 1 / cot θ
---
3. Quotient Identities
tan θ = sin θ / cos θ
cot θ = cos θ / sin θ
---
4. Pythagorean Identities
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
---
5. Trigonometric Values for Standard Angles
(i) sin θ values
θ : 0°, 30°, 45°, 60°, 90°
sin : 0, 1/2, 1/√2, √3/2, 1
(ii) cos θ values
θ : 0°, 30°, 45°, 60°, 90°
cos : 1, √3/2, 1/√2, 1/2, 0
(iii) tan θ values
θ : 0°, 30°, 45°, 60°, 90°
tan : 0, 1/√3, 1, √3, ∞
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6. Trigonometric Ratios of Complementary Angles
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
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7. Trigonometric Identities (Important)
sin 2θ = 2 sin θ cos θ
cos 2θ = cos²θ – sin²θ
tan 2θ = 2 tan θ / (1 – tan²θ)
---
8. Height & Distance Formulas
Used in Class 10 Applications:
tan θ = Height / Distance
cot θ = Distance / Height
---
Conclusion (Exam-style)
Trigonometry mainly depends on ratios, standard angles, and identities.
If you remember:
⭐ sin–cos pair,
⭐ tan = sin/cos,
⭐ sin² + cos² = 1,
then the entire chapter becomes easy and scoring.
---
If you want, I can send:
✅ Colourful PDF Notes
✅ Full Trigonometry Formula Chart (HD)
✅ Important 50 MCQs + Answers
Just tell me “Trigonometry chart”, or “MCQ test”.
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