Prove sin x tan x = sec x - cos x
2 Answers
hala718 | High School Teacher | (Level 1) Educator Emeritus
sin(x)*tan(x) = sec(x) - cos(x)
We will start from the left side.
==> We know that tan(x) = sin(x)/cos(x)
==> sin(x)*tan(x) = sin(x)*sin(x)/ cos(x)
= sin^2 x/ cos(x)
But we know that sin^2 x = 1- cos^2 x
==> sin(x)*tan(x) = (1-cos^2 x) / cosx
= 1/cos(x) - cos^2 x / cosx
But 1/cosx = sec(x)
==> sin(x)*tan(x) = sec(x) - cos(x).........q.e.d
lochana2500 | Student, Undergraduate | (Level 1) Valedictorian
L:H:S ≡ sin x tan x
= sinx (sinx/cosx)
= sin²x/cosx
= (1-cos²x)/cosx
= 1/cosx - cos²x/cosx
= secx - cosx
= R:H:S