Question

यदि `(1-sinA)(1-sinB)(1-sinC)=(1+sin A)(1+sin B)(1+sinC),` तो सिद्ध कीजिए प्रत्येक का मान `pm cos A cos B cos C` होगा ।

Answer 1

माना`" "x=(1-sina)(1-sinB)(1-sin C)=(1+sin A)(1+sinB)(1+sinC)`
अब `" "x^(2)=x.x`
`" "=(1-sinA)(1-sinB)(1-sinC).(1+sinA)(1+sinB)(1+sinC)`
`" "=(1-sin^(2)A)(1-sin^(2)B)(1-sin^(2)C)`
`" "=cos^(2)A.cos^(2)B.cos^(2)C`
`rArr" "x=sqrt(cos^(2)Acos^(2)Bcos^(2)C)`
`" "=pm cos A cos B cos C`