Trigonometric Functions | 1st PUC 11th CBSE | Mathematics | Part 4 of 10

In this comprehensive video, we break down the essential trigonometric identities: tan(x ± y) and cot(x ± y), which are crucial for solving complex problems in trigonometry and simplifying expressions.

The tan(x ± y) identity is expressed as:
tan(x + y) = tanx + tany / 1 - tanx . tany
tan(x - y) = tanx - tany / 1 + tanx . tany

For cotangent:
cot(x + y) = cotx . coty - 1 / cotx + coty
cot(x - y) = cotx . coty + 1 / coty - cotx

In this tutorial, Babu Sir, with over 25 years of experience, walks you through each step of the derivations, offering detailed examples and problem-solving tips. These identities are critical for students preparing for CET, JEE Mains, or board exams, and mastering them will boost your confidence in solving trigonometric problems.

What you’ll learn:
Core Concepts: Step-by-step derivation of tan(x ± y) and cot(x ± y) identities.
Practical Applications: Simplifying trigonometric expressions and solving complex equations involving angles.
Problem-Solving Strategies: Tips to ace questions involving these identities in CET, JEE, and Board Exams.
Don't miss this must-watch video for students looking to excel in mathematics. Mastering the tan(x ± y) and cot(x ± y) formulas is key to understanding more advanced mathematical concepts and excelling in exams.

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TIMESTAMPS:
00:00 - Intro
01:23 - sin(𝑥 + 𝑦) = 𝑠𝑖𝑛 𝑥 𝑐𝑜𝑠 𝑦 + 𝑐𝑜𝑠𝑥 𝑠𝑖𝑛𝑦, sin(𝑥 - 𝑦) = 𝑠𝑖𝑛 𝑥 𝑐𝑜𝑠 𝑦 - 𝑐𝑜𝑠 𝑥 𝑠𝑖𝑛 𝑦
(NCERT , Topic 3.4, example 7 & 8 , Page no. 59)
02:09 - cos(x+y) = cos x cos y - sinx sin y, cos (x-y) = cos x cos y + sin x sin y
(NCERT , Topic 3.4, example 3, 4 , Page no. 58&59)
02:57 - If none of the angles, x, y & (x + y)is an odd multiple of 𝜋 / 2, then tan(x + y) = tanx+tany / 1−𝑡𝑎𝑛𝑥 𝑡𝑎𝑛y (NCERT , Topic 3.4, example 10, Page no. 60)
07:39 - Prove tan ( x-y ) = tanx - tany / 1 + tan x tan y
(NCERT , Topic 3.4, example 11, Page no. 60)
11:04 - Prove cot ( x - y ) = cot x cot y + 1 / cot y - cot x
(NCERT , Topic 3.4, example 13, Page no. 61)
15:23 - If none of the angles, x, y & (x + y) is a multiple of 𝜋, then cot(x + y) = cotx coty−1 𝑐𝑜𝑡𝑦+𝑐𝑜𝑡x
(NCERT , Topic 3.4, example 12, Page no. 60 & 61)

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