ICSE Class 10 Answered

Tan²A—Tan²B=(sin²A—sin²B) ÷cos²A×cos²B

Asked by Mmanjima7 | 25 Apr, 2019, 12:11: PM

Expert Answer

begin mathsize 16px style To space prove space that colon tan squared straight A space space minus space tan squared straight B space equals space fraction numerator sin squared straight A space space minus space sin squared straight B over denominator cos squared straight A space space cross times space cos squared straight B end fraction straight L. straight H. straight S space equals space tan squared straight A space space minus space tan squared straight B space space space space space space space space space space space equals space fraction numerator sin squared straight A over denominator cos squared straight A end fraction space minus fraction numerator sin squared straight B over denominator cos squared straight B end fraction space space space space space space space space space space space space equals space fraction numerator sin squared Acos squared straight B space minus sin squared Bcos squared straight A space over denominator cos squared Acos squared straight B end fraction space space space space space space space space space space space equals fraction numerator sin squared straight A open parentheses 1 space minus space space sin squared straight B close parentheses space minus sin squared straight B open parentheses 1 space minus space space sin squared straight A close parentheses space over denominator cos squared Acos squared straight B end fraction space space space space space space space space space space space equals fraction numerator sin squared straight A space minus space sin squared Asin squared straight B space minus space sin squared straight B space plus sin squared Asin squared straight B space over denominator cos squared Acos squared straight B end fraction space space space space space space space space space space space equals fraction numerator sin squared straight A space space minus space sin squared straight B space space over denominator cos squared Acos squared straight B end fraction space space space space space space space space space space space equals space straight R. straight H. straight S Hence space proved. end style

Answered by Yasmeen Khan | 25 Apr, 2019, 12:41: PM

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