Introduction
Trigonometric identities often confuse Class 10 students, but they are actually the simplest once you know the logic. These identities are the backbone of trigonometry and are repeatedly used in exams. In this blog, I’ll walk you through the proof of three trigonometric identities with clear steps and examples. You’ll also find a video lesson embedded for easier understanding.
📹 Watch my step-by-step video here:
What Are Trigonometric Identities?
They are equations that are true for all values of an angle.
Based on right-angled triangle properties.
Every advanced trigonometric formula comes from these three basics.
These identities are:
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = csc²θ
✅ Proof of Identity 1: sin²θ + cos²θ = 1
Start with Pythagoras theorem: hypotenuse² = base² + perpendicular².
Divide by hypotenuse².
Result: sin²θ + cos²θ = 1
✅ Proof of Identity 2: 1 + tan²θ = sec²θ
tanθ = sinθ / cosθ, secθ = 1 / cosθ.
Divide the first identity by cos²θ.
Result: 1 + tan²θ = sec²θ
✅ Proof of Identity 3: 1 + cot²θ = csc²θ
cotθ = cosθ / sinθ, cscθ = 1 / sinθ.
Divide the first identity by sin²θ.
Result: 1 + cot²θ = csc²θ
Why Should You Learn These Proofs?
Direct questions in Class 10 board exams.
Makes solving trigonometric equations faster.
Foundation for Class 11 and 12 Maths.
📌 Tip: Practice at least 5 questions daily from NCERT and previous year papers.
Common Mistakes Students Make
Writing sinθ + cosθ = 1 instead of squaring terms.
Confusing secθ with cscθ.
Skipping the division step when deriving the 2nd and 3rd identities.
Conclusion
Trigonometric identities are not difficult if you understand the logic and practice step-by-step. Watch the video lesson above for detailed explanation and examples.
📌 Author Bio :
Aman Sir – Maths Vidya Institute
Aman Sir has over 14+ years of experience teaching Class 8–12 CBSE Mathematics online and offline. As the founder of Maths Vidya Institute, he has helped many students secure top scores in board exams through personalized teaching methods, conceptual clarity, and exam-oriented practice.
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