Question

Prove that
`(i) (sin^(2)A cos^(2)B - cos^(2)A sin^(2) B )=(sin^(2)A- sin^(2)B) `
`(ii) (tan^(2)A sec^(2)B - sec^(2)A tan^(2)B)=(tan^(2)A- tan^(2)B) `

Answer 1

We have
`(i) LHS = (sin^(2)A cos^(2)B - cos^(2)A sin^(2) B )`
`= sin^(2)A(1- sin^(2)B)-(1- sin^(2)A)sin^(2)B `
` = sin^(2)A - sin^(2)B = RHS. `
`(ii) LHS = (tan^(2)A sec^(2)B - sec^(2)A tan^(2)B) `
` =tan^(2)A(1+tan^(2)B) - (1+ tan^(2)A)tan^(2)B `
` = (tan^(2)A - tan^(2)B) = RHS. `