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Simplify the expression as much as possible. Simplify the expression as much as possible.
sec(x) + sin(x) tan(-x)
Solution
sec(x) +(sin(x)*tan(-x))
=sec(x) +(sin(x)*(-tan(x)))
=sec(x) -(sin(x)tan(x))
=(1/cos(x)) -(sin(x)(sin(x)/cos(x)))
=(1/cos(x)) -(sin2(x)/cos(x))
=(1 -sin2(x))/cos(x)...................................[since sin2(x)+cos2(x)=1 is an identity]
=(cos2(x))/cos(x)
=cos(x)

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  • 1. Simplify the expression as much as possible. Simplify the expression as much as possible. sec(x) + sin(x) tan(-x) Solution sec(x) +(sin(x)*tan(-x)) =sec(x) +(sin(x)*(-tan(x))) =sec(x) -(sin(x)tan(x)) =(1/cos(x)) -(sin(x)(sin(x)/cos(x))) =(1/cos(x)) -(sin2(x)/cos(x)) =(1 -sin2(x))/cos(x)...................................[since sin2(x)+cos2(x)=1 is an identity] =(cos2(x))/cos(x) =cos(x)