trigonometric identities😍| examples | introduction to trigonometry🔥| chapter - 8 | NCERT #maths

trigonometric identities😍| examples | introduction to trigonometry🔥| chapter - 8 | NCERT #maths introduction, chapter 8 introduction, class 10 chapter 8 introduction, class 10 maths chapter 8 introduction, introduction to trigonometry, trigonometry, trigonometric ratios on specific angles, trigonometric ratios, trigonometric identities, trigonometry applications, application of trigonometry, class 10 maths, maths by faiz sir, infinix classes, maths infinix classes, faiz sir infinix classes, right angled triangle, pythagorus theorem, why only six trigonometric ratios, use of pythagorus theorem, uses of trigonometry, why trigonometry, meaning of trigonometry, trigonometry concept, ssc cgl maths syllabus, ssc maths syllabus, maths syllabus, cbse board maths syllabus, bihar board maths syllabus, trigonometry important concept, trigonometry important questions, sin theta, cos theta, tan theta, cosec theta, sec theta, cot theta, trigonometric identities, #trigonometryclass10 #trignometry #trigonometrymaths #trigonometric #trigonometri #trigonometricfunctions #trigonometricratios #trigonometricratiosandidentities #trigonometricratio #trigonometric_functions #mathsbyfaizsir #infinixclasses #faizsir #maths #maths_concept #maths_class_guru_sir #maths_magic #mathsshorts #trigonometria #sincostan #trigonometricidentities #class10thmaths #class10th #class10thmath #clas10th #class10thobjective #class10th_maths #class10thmathojectivequestion #class10th_boardexam #cbsemaths #cbseboard #cbseclass10 #biharboard #biharboardexam #biharboardsubjectivequestions #biharboardmaths #bseb #angles #trigonometrymaths Trigonometric Identities: 1) cos^2 A + sin^2 A = 1 2) 1 + tan^2 A = sec^2 A 3) cot^2 A + 1 = cosec^2 A Example 9 : Express the ratios cos A, tan A and sec A in terms of sin A. Example 10 : Prove that sec A (1 – sin A)(sec A + tan A) = 1. Example 11 : Prove that (cot A – cos A) /(cot A + cos A) = (cosec A – 1) /(cosec A + 1) . Example 12 : Prove that (𝐬𝐢𝐧⁡𝜽 − 𝐜𝐨𝐬⁡𝜽 + 𝟏)/(𝐬𝐢𝐧⁡𝜽 + 𝐜𝐨𝐬⁡𝜽 − 𝟏) = 𝟏/(𝐬𝐞𝐜 𝛉 − 𝐭𝐚𝐧 𝛉) using the identity sec2 θ = 1 + tan2 θ. Trigonometry is a branch of mathematics focused on the relationships between the angles and sides of triangles, particularly right-angled triangles. It involves studying trigonometric ratios (sine, cosine, tangent, etc.) and their applications in solving problems related to angles and distances. Key Concepts: Right-Angled Triangles: Trigonometry primarily deals with right-angled triangles, where one angle is 90 degrees. Trigonometric Ratios: These ratios (sine, cosine, tangent, cotangent, secant, cosecant) express the relationships between the sides of a right triangle and its angles. Sine (sin): Opposite side / Hypotenuse Cosine (cos): Adjacent side / Hypotenuse Tangent (tan): Opposite side / Adjacent side Trigonometric Identities: Equations that are true for all values of the variables involved. They are used to simplify expressions, solve equations, and prove other identities. Angles: Angles in trigonometry are typically measured in degrees or radians. Applications: Trigonometry has numerous real-world applications in various fields, including: Navigation: Determining distances and directions. Engineering: Designing structures, calculating forces, and analyzing motion. Physics: Studying waves, oscillations, and other periodic phenomena. Astronomy: Measuring distances to celestial objects. Surveying: Mapping and measuring land. Computer Graphics: Creating and manipulating images. In essence, trigonometry provides a powerful set of tools for understanding and solving problems involving triangles and their relationships to angles and distances.