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summary of this topic

### Trigonometric Identities for compound angles

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Home

Some Results

Quickly derive the identities. No need to memorize.

»  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))

### More results for trigonometric values of Compound Angles

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

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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

Progress

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.

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