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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.

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

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

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

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*summary of this topic*

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Some Results

» Use `(a+b)(a-b)``=a^2-b^2`

`sin(A+B)sin(A-B)`

`cos(A+B)cos(A-B)`

`tan(A+B)tan(A-B)`

`cot(A+B)cot(A-B)`

» `3` angles

`sin(A+B+C)``=sin(A+(B+C))`

`cos(A+B+C)``=cos(A+(B+C))`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

`sin(A+B)sin(A-B)`

`quad quad = sin^2 A - sin^2 B`

`quad quad = cos^2 B - cos^2 A`

`cos(A+B)cos(A-B)`

`quad quad = cos^2 A - sin^2 B`

`quad quad = cos^2 B - sin^2 A`

`tan(A+B) tan(A-B)`

`quad quad = (tan^2 A - tan^2 B)/(1-tan^2 A tan^2 B)`

`cot(A+B) cot(A-B)`

`quad quad = (1-cot^2 A cot^2 B)/(cot^2 A - cot^2 B)`

`sin(A+B+C)`

`quad = sinA cosB cos C + cosA sinB cos C`

`quad quad quad + cosA cosB sinC - sinA sinB sinC `

`cos(A+B+C)`

`quad = cosA cosB cos C - sinA sinB cos C`

`quad quad quad - sinA cosB sinC - cosA sinB sinC `

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

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In this page, some additional results involving trigonometric function of compound angle is discussed.

Starting on learning "More results for trigonometric values of Compound Angles". ;; In this page, some additional results involving trigonometric function of compound angle is discussed.

Consider `sin(A+B)sin(A-B)`

`quad = (sinA cosB + cosA sinB)`

`quad quad quad xx (sinA cosB - cosA sinB)`

`quad = sin^2 A cos^2B - cos^2A sin^2B`

substitute `cos^2 B = (1-sin^2 B)`

`quad = sin^2A - sin^2B xx(sin^2 A+cos^2 A)`

`quad = sin^2A - sin^2B`

substitute `sin^2A = (1-cos^2 A)`

`quad = cos^2B - cos^2A(cos^2B+sin^2B)`

`quad = cos^2 B - cos^2 A`

Consider `cos(A+B)cos(A-B)`

`quad = (cosA cosB - sinA sinB)`

`quad quad quad xx (cosA cosB + sinA sinB)`

`quad = cos^2 A cos^2B - sin^2A sin^2B`

substitute `cos^2 B = (1-sin^2 B)`

`quad = cos^2A - sin^2B xx(sin^2 A+cos^2 A)`

`quad = cos^2A - sin^2B`

substitute `sin^2B = (1-cos^2 B)`

`quad = cos^2B(cos^2A+sin^2A)-sin^2A`

`quad = cos^2 B - sin^2 A`

`tan(A+B) tan(A-B)`

substitute

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

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

and multiply numerators and denominators of them

`quad quad = (tan^2 A - tan^2 B)/(1-tan^2 A tan^2 B)`

`cot(A+B) cot(A-B)`

Substitute

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

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

and multiply numerator and denominator

`quad quad = (1-cot^2 A cot^2 B)/(cot^2 A - cot^2 B)`

`sin(A+B+C)`

`quad = sin( (A+B)+ C)`

`quad = sin(A+B)cos C + cos(A+B)sinC`

`quad = sinA cosB cos C + cosA sinB cos C`

`quad quad quad + cosA cosB sinC - sinA sinB sinC `

`cos(A+B+C)`

`quad = cos( (A+B)+ C)`

`quad = cos(A+B)cos C - sin(A+B)sinC`

`quad = cosA cosB cos C - sinA sinB cos C`

`quad quad quad - sinA cosB sinC - cosA sinB sinC `

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

** More results of Trigonometric values for compound Angles** `sin(A+B)sin(A-B)`

`quad quad = sin^2 A - sin^2 B`

`quad quad = cos^2 B - cos^2 A`

`cos(A+B)cos(A-B)`

`quad quad = cos^2 A - sin^2 B`

`quad quad = cos^2 B - sin^2 A`

`tan(A+B) tan(A-B)`

`quad quad = (tan^2 A - tan^2 B)/(1-tan^2 A tan^2 B)`

`cot(A+B) cot(A-B)`

`quad quad = (1-cot^2 A cot^2 B)/(cot^2 A - cot^2 B)`

`sin(A + B + C) = sin((A+B)+C)`

`cos(A + B + C) = cos((A+B)+C)`

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

*your progress details*

Progress

*About you*

Progress

Consider sine A + B multiplied sine A minus B. With modifications, two results are derived.

sine A + B multiplied sinA minus B ;; equals sin squared A minus sine squared B ;; and equals cos squared B squared cos squared A

Consider cos A + B multiplied cos A minus B. With modifications, two results are derived.

cos A + B multiplied cos A minus B ;; equals cos squared A minus sine squared B ;; and equals cos squared B squared minus sine squared A

Consider tan A+B multiplied by tan A minus B. With modifications, a result is derived as follows.

tan a + b multiplied tan a minus B = tan squared A minus tan squared B divided by 1 minus tan squared A tan squared b.

consider cot A + B multiplied by cot A minus B. With modifications, a result is derived as follows

cot A + B multiplied cot A minus B equals; 1 minus cot squared A cot squared B divided by cot squared A minus cot squared B

consider sine A + B + C. Using previous results, a result is derived.

sine A + B + C equals, sine A cos B cos C, + cos A sine B cos C, + cos A cos B sine C minus sine sine B sine C.

consider cos A + B + C. Using previous results, a result is derived.

cos A + B + C equals cos A cos B cos C minus sine A sine B cos C minus sine A cos B sine C minus cos A sine B sine C

More results of Trigonometric values for compound angles are given.