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CBSE Class 11-science Answered

Prove that:
(i) cos(A-B)= cosAcosB + sinAsinB
(ii)cos(A+B)= cosAcosB - sinAsinB
Asked by sunil2791 | 14 Nov, 2017, 07:46: PM
answered-by-expert Expert Answer
begin mathsize 16px style We space know space that space equal space chords space of space straight a space circle space makes space equal space angles at space the space centre space and space chords space straight P subscript 0 straight P subscript 3 space and space straight P subscript 1 straight P subscript 2 space subtend space equals space angles space at space the space centre. space straight P subscript 0 straight P subscript 3 space equals space straight P subscript 1 straight P subscript 2 Using space distance space formula comma square root of open square brackets cos open parentheses straight A minus straight B close parentheses squared minus 1 close square brackets plus sin squared open parentheses straight A minus straight B close parentheses end root equals square root of open parentheses cosB minus cosA close parentheses squared plus open parentheses sinB minus sinA close parentheses squared end root After space solving space you space will space get space cos left parenthesis straight A minus straight B right parenthesis equals cosAcosB plus sinAsinB For space the space second space one space we space can space solve space using space above space formula cos left parenthesis straight A plus straight B right parenthesis equals cos open square brackets straight A minus left parenthesis negative straight B right parenthesis close square brackets cos left parenthesis straight A plus straight B right parenthesis equals cosAcos left parenthesis negative straight B right parenthesis plus sinAsin left parenthesis negative straight B right parenthesis cos left parenthesis straight A plus straight B right parenthesis equals cosAcosB minus sinAsinB space space space space space space space space space space space space space space space space cos left parenthesis negative straight A right parenthesis equals cosA space and space sin left parenthesis negative straight B right parenthesis equals negative sinB end style
Answered by Sneha shidid | 07 Dec, 2017, 10:20: AM

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