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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.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

Welcome to **nub****trek**.

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The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

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exercise.

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*summary of this topic*

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Compound angles of tan & cot

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

» `cot(A+-B) = (cos(A+-B))/(sin(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.

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.