Question

The value of the expression `(cos^(2)23^(@)-sin^(2)67^(@))` is positive.

Answer 1

False
`cos^(2)23^(@)-sin^(2)67^(@)=(cos23^(@)+sin67^(@)) [therefore (a^(2)-b^(2)=(a-b)(a+b)]`
`[cos23^(@)-sin(90^(@)-23^(@))](cos23^(@)+sin67^(@))`
`(cos23^(@)-cos23^(@))(cos23^(@)+sin67^(@))` `[therefore sin(90^(@)-theta)=cos theta]`
`=0.(cos23^(@) + sin67^(@))=0`
Which may be either positive or negative.