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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

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User Guide

Welcome to nubtrek.

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learn.

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User Guide

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nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

nub,

trek,

jogger,

exercise.

User Guide

nub is the simple explanation of the concept.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about.

User Guide

trek is the step by step exploration of the concept.

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step.

User Guide

jogger provides the complete mathematical definition of the concepts.

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen.

User Guide

exercise provides practice problems to become fluent in the concepts.

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge.

summary of this topic

### Trigonometric Identities for compound angles

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Compound angles of tan & cot

Quickly derive the identities. No need to memorize.

»  tan(A+-B) = (sin(A+-B))/(cos(A+-B))

»  cot(A+-B) = (cos(A+-B))/(sin(A+-B))

### Compound Angles: tan(A+B) and tan(A-B)

plain and simple summary

nub

plain and simple summary

nub

dummy

tan(A+B) = (tan A + tan B)/(1- tan A tan B)
tan(A-B) = (tan A - tan B)/(1+ tan A tan B)

cot(A+B) = (cot A cot B -1)/(cot A + cot B)
cot(A-B) = (-cot A cot B -1)/(cot A - cot B)

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, expressing tan(A + B) and tan(A-B) in terms of tan A and tan B is explained.

Keep tapping on the content to continue learning.
Starting on learning "tan a + b and tan a minus b". ;; In this page, expressing tan(A + B) and tan A minus B in terms of tan A and tan B is explained.

Proof for tan(A+B) and tan(A-B) using previous results and algebra of trigonometric functions.

tan(A+B)
quad quad = (sin(A+B))/(cos(A+B))
quad quad = (sinA cosB + cosA sinB)/(cosA cosB - sinA sinB)
dividing numerator and denominator by cosA cosB
quad quad = (tan A + tan B)/(1 - tan A tan B)

tan(A-B)
quad quad = tan(A+(-B))
quad quad = (tan A - tan B)/(1 + tan A tan B)

Proof for cot(A+B) and cot(A-B) using previous results and algebra of trigonometric functions.

cot(A+B)
quad quad = (cos(A+B))/(sin(A+B))
quad quad = (cosA cosB - sinA sinB)/(sinA cosB + cosA sinB)
dividing numerator and denominator by sinA sinB
quad quad = (cot A cot B -1)/(cot A + cot B)

cot(A-B)
quad quad = cot(A+(-B))
quad quad = (-cot A cot B -1)/(cot A - cot B)

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Trigonometric Identities for compound Angles

sin(A+B)=sinA cosB + cosA sinB
sin(A-B)=sinA cosB - cosA sinB
cos(A+B)=cosA cosB - sinA sinB
cos(A-B)=cosA cosB + sinA sinB

tan(A+B) = (tan A + tan B)/(1- tan A tan B)
tan(A-B) = (tan A - tan B)/(1+ tan A tan B)

cot(A+B) = (cot A cot B -1)/(cot A + cot B)
cot(A-B) = (-cot A cot B -1)/(cot A - cot B)

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

your progress details

Progress

About you

Progress

Proof for tan A + B and tan A minus B using previous results and algebra of trigonometric functions:
tan a + b = tan a + tan b divided by 1 minus tan a tan b.;; tan a minus b = tan a minus tan b divided by 1 plus tan a tan b
Proof for cot A + B and cot A minus B using previous results and algebra of trigonometric functions:
cot a + b = cot A cot B minus 1 divided by cot A plus cot B.;; cot a minus b = minus cot A cot B minus 1 divided by cot A minus cot B
Trigonometric identities for compound angles are given. No need to memorize these formulas. Follow the logic of deriving all from sine A + B. Every time you use the formula, follow the logic to derive. The more time you spend in solving problems, you will better remember these formulas.

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