Question

$(si{n}^{2}Aco{s}^{2}B-co{s}^{2}Asi{n}^{2}B)=$

• A. $si{n}^{2}A+si{n}^{2}B$
• B. $si{n}^{2}A-si{n}^{2}B$
• C. $co{s}^{2}A-si{n}^{2}B$
• D. $co{s}^{2}A+si{n}^{2}B$

Answer 1

The correct option is B $si{n}^{2}A-si{n}^{2}B$

$=(si{n}^{2}Aco{s}^{2}B-co{s}^{2}Asi{n}^{2}B)$

$=si{n}^{2}A(1-si{n}^{2}B)-(1-si{n}^{2}A)si{n}^{2}B$

$=1.si{n}^{2}A-si{n}^{2}A.si{n}^{2}B-1.si{n}^{2}B+si{n}^{2}A.si{n}^{2}B$

$=si{n}^{2}A-si{n}^{2}B$