Trigonometry Formulas Class 10 — Trikonamiti Notes, Simple Hindi Mein

Trigonometry formulas Class 10 in Hindi — yeh notes NCERT Class 10 Maths ke chapter “Introduction to Trigonometry” (Trikonamiti ka Parichay) par based hain. Board exam mein is chapter se identities prove karne aur standard angles par based 3-5 marks ke sawaal pakke aate hain. Formulas yaad ho gaye to chapter aasaan hai.

Trigonometry Kya Hai?

• Trigonometry (Trikonamiti) ka matlab hai: triangle ke sides aur angles ke beech ke sambandh ka adhyayan.
• Hum right-angled triangle (samkon tribhuj — jismein ek angle 90° ka ho) par kaam karte hain.
• Ek acute angle θ (theta) ke liye triangle ki 3 sides ke naam:
• Hypotenuse (Karn): 90° angle ke saamne wali sabse lambi side.
• Perpendicular (Lamb): angle θ ke saamne wali side.
• Base (Aadhaar): angle θ ke paas wali side (hypotenuse ko chhodkar).

6 Trigonometric Ratios (Trikonmitiya Anupaat)

Trigonometry formulas class 10 in hindi mein angle θ ke liye 6 ratios hote hain — inhe isi order mein yaad karein:

• sin θ = Perpendicular / Hypotenuse (Lamb / Karn)
• cos θ = Base / Hypotenuse (Aadhaar / Karn)
• tan θ = Perpendicular / Base (Lamb / Aadhaar)
• cot θ = Base / Perpendicular = 1 / tan θ
• sec θ = Hypotenuse / Base = 1 / cos θ
• cosec θ = Hypotenuse / Perpendicular = 1 / sin θ

Yaad Rakhne Ki Trick

“Pandit Badri Prasad, Har Har Bole” — pehle akshar se:

• Pandit = Perpendicular, Badri = Base, Har = Hypotenuse
• sin = P/H, cos = B/H, tan = P/B (baaki teen inke ulte)

Standard Angles Table (0°, 30°, 45°, 60°, 90°)

Trigonometry formulas class 10 in hindi mein yeh table exam mein sabse zyada kaam aati hai — ise likh-likh kar yaad karein:

• sin: 0°, 30°, 45°, 60°, 90° → 0, 1/2, 1/√2, √3/2, 1
• cos: 0°, 30°, 45°, 60°, 90° → 1, √3/2, 1/√2, 1/2, 0
• tan: 0°, 30°, 45°, 60°, 90° → 0, 1/√3, 1, √3, not defined

Table Yaad Karne Ki Trick

• sin ki values: 0, 1, 2, 3, 4 likho → har ek ka square root lo → 2 se divide karo → 0, 1/2, 1/√2, √3/2, 1.
• cos ki values sin ki ulti order mein hain (1, √3/2, 1/√2, 1/2, 0).
• tan = sin / cos — table se hi nikaal lo, alag se yaad karne ki zaroorat nahi!

Trigonometric Identities (Sarvasamikaayein)

Yeh 3 identities prove karne wale sawalon mein sabse zyada aati hain:

1. sin²θ + cos²θ = 1
2. 1 + tan²θ = sec²θ
3. 1 + cot²θ = cosec²θ

Identities Kaise Yaad Rakhein?

• Pehli identity Pythagoras theorem (a² + b² = c²) se aati hai — dono sides ko hypotenuse² se divide kar do.
• Doosri aur teesri pehli se hi nikalti hain: pehli ko cos²θ se divide karo to (2) milegi, sin²θ se divide karo to (3) milegi.
• Exam tip: “prove that” wale sawaal mein hamesha ek side (aam taur par complicated wali) se shuru karo aur identities lagakar doosri side tak pahuncho.

Complementary Angles (Poorak Kon)

Trigonometry formulas class 10 in hindi mein complementary angles ke ye formulas yaad rakho:

• sin(90° − θ) = cos θ
• cos(90° − θ) = sin θ
• tan(90° − θ) = cot θ
• Yaad rakho: 90° mein se angle ghataane par sin↔cos, tan↔cot, sec↔cosec badal jaate hain.

Heights and Distances (Unchaai Aur Doori) — Basic Idea

Trigonometry formulas class 10 in hindi ka practical use heights and distances ke sawalon mein hota hai:

• Angle of elevation: neeche se upar dekhne par banta angle.
• Angle of depression: upar se neeche dekhne par banta angle.
• Diagram zaroor banaao: perpendicular/base ki pehchaan karo, sahi ratio (tan aksar kaam aata hai) lagao, standard angle ki value rakho.

Trigonometry Formulas Class 10 — Revision Points

1. 6 ratios ke formulas aur “Pandit Badri Prasad” trick.
2. Standard angles table — sin/cos/tan ki values bina dekhe likh sako.
3. Teeno identities aur unka aapas ka sambandh.
4. tan 90° defined nahi hota (not defined) — yeh MCQ mein aata hai.
5. Prove wale sawalon mein ek side se shuru karke identities apply karo.
6. Heights-distances mein pehle sahi diagram, phir sahi ratio.

Trigonometry Formulas Class 10 — Practice Questions

1. Prove karo: (1 + tan²θ) = sec²θ (2 marks)
2. Agar sin A = 1/2 ho to cos A aur tan A ka maan gyaat karo. (3 marks)
3. Evaluate: 2tan²45° + cos²30° − sin²60° (3 marks)
4. Ek 30m unche tower ke top se zameen par khade vyakti ka angle of depression 30° hai — doori gyaat karo. (4 marks)

Trigonometry formulas class 10 in hindi ke baad Class 10 Science ke notes ke liye Human Heart Notes padhein. Saare study notes https://jagatindia.com/category/students/ par milenge.