Given cos 40=m and sin 10=n,can u please express sin 50 in terms of m and n?

1 Answer
Jul 8, 2017

sin50=sin(40+10)sin50=sin(40+10)

=sin40cos10+cos40sin10=sin40cos10+cos40sin10

=sqrt((1-m^2)) * sqrt((1-n^2))+mn=(1m2)(1n2)+mn

Explanation:

Use

sin(A+B)= sinAcosB+cosAsinBsin(A+B)=sinAcosB+cosAsinB

and

(cos40)^2+(sin40)^2=1(cos40)2+(sin40)2=1

or

(sin40)^2=1-(cos40)^2(sin40)2=1(cos40)2

or

sin40=sqrt([1-(cos40)^2])sin40=[1(cos40)2]

or

sin40=sqrt((1-m^2))sin40=(1m2)

Similarly,

cos40=sqrt((1-n^2))cos40=(1n2)