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Thought-Process to Discover Knowledge

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User Guide    

nub is the simple explanation of the concept.

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exercise provides practice problems to become fluent in the concepts.

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summary of this topic

Trigonometric Identities for compound angles

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

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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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