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If (1+sinA)( 1+sinB)(1+sinC) = (1-sinA)(...

If (1+sinA)( 1+sinB)(1+sinC) = (1-sinA)(1-sinB)(1-sinC), then prove that the value of each side = `+-cos A cosB cosC`,

Text Solution

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Multiplying both sides by `(1-sinA)(1-sinB)(1-sinC)`, we get
`(1-sin^2A)(1-sin^2B)(1-sin^2C)`
`= (1-sinA)^2(1-sinB)^2(1-sinC)^2`
`rArr (1-sinA)(1-sinB)(1-sinC)`
`=pmcosAcosBcosC`
Similrly,`(1+sinA)(1+sinB)(1+sinC)`
`=pmcoAcosBcosC`
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