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Thought-Process to Discover Knowledge

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

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

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**.

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

think,

figure-out, &

learn.

**Just keep tapping** (or clicking) on the content to continue in the trail and learn. continue

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

think,

figure-out, &

learn.

To make best use of nubtrek, understand what is available.

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

nub,

trek,

jogger,

exercise.

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

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. continue

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. continue

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. continue

*summary of this topic*

Voice

Voice

Home

sin(A-B), cos(A+B), cos(A-B)

» `sin(A+B)` Proven result

» `sin(A-B) = sin(A+(-B))`

» `cos(A+B) ``= sin((90-A) -B)`

» `cos(A-B)``= sin((90-A)+B)`

Geometrical Proof

» `sin(A-B)` from `bar(RT)=bar(PQ1)`

» `cos(A-B)` from `bar(RS)=bar(PQ)`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

`sin(A-B)=sinA cosB - cosA sinB`

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

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

You are learning the free content, however do shake hands with a coffee to show appreciation.

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In this page, a simple proof, based on the earlier result of `sin(A+B)`, is explained for expressing `cos(A+B)`, `sin(A-B)`, `cos(A-B)` in terms of `sinA`, `sinB`, `cosA` , and `cosB`.

Starting on learning "cos A +B, sine A minus B, cos A minus B". ;; In this page, a simple proof based on the earlier result of sine A + B, is explained for expressing cos A + B, sine A minus B, cos A minus B, in terms of sine A, sine B, cos A , and cosB.

It was geometrically proven that `cos(A+B)=cosA cosB - sinA sinB`. For the same result, we can work out a proof using algebra of trigonometric functions.

`cos(A+B)`

`quad quad = sin(90-A-B)`

`quad quad = sin[(90-A) + (-B)]`

`quad quad = sin(90-A)cos(-B)+cos(90-A)sin(-B)`

`quad quad = cosA cosB - sinA sinB`

To calculate trigonometric values for compound angle, we will switch to using the proofs with algebra of trigonometric functions, as it is simpler. But, equivalently a geometrical proof can be worked out.

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

`sin(A-B)`

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

`quad quad = sinA cos(-B)+ cosA sin(-B)`

`quad quad = sinA cosB - cosA sinB`

`cos(A-B)`

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

`quad quad = cosA cos(-B) - sinA sin(-B)`

`quad quad = cosA cosB + sinA sinB`

Geometrical proof for `sin(A-B)` and `cos(A-B)` is outlined below. equate square of chord lengths to derive the result given.

`bar(RT)^2 = bar(PQ1)^2`

`=> sin(A-B) = sinA cosB - cosA sinB `

`bar(RS)^2 = bar(PQ)^2`

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

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

Compute `sin75`.

- cannot compute as `75^@` is not a standard angle
- consider `75^@` as sum of standard angles `45^@` and `30^@`

The answer is 'consider `75^@` as sum of standard angles `45^@` and `30^@`'.

`sin75`

`quad = sin(45+30)`

`quad = sin45cos30 + cos45sin30`

`quad = (1+ sqrt(3))/(2sqrt(2))`

*your progress details*

Progress

*About you*

Progress

It was geometrically proven that cos A+ B = cos A cos B minus sine A sine B. For the same result, we can work out a proof using algebra of trigonometric functions.

To calculate trigonometric values for compound angle, we will switch to using the proofs with algebra of trigonometric functions, as it is simpler. But, equivalently a geometrical proof can be worked out.

Proof for sine A minus B and cos A minus B using previous results and algebra of trigonometric funtions is given.

Geometrical proof for sine A minus B and cos A minus B is outlined below.

sine A minus B = sine A cos B minus cos A sine B;; cos A minus B = cos A cos B plus sine A sine B.

compute sine 75 degree.

cannot;not;compute

cannot compute as 75 degree is not a standard angle

consider;sum;45;30

consider 75 degree as sum of standard angles 45 degree and 30 degree

The answer is "consider 75 degree as sum of standard angles 45 degree and 30 degree"