Question
if cos=2/5, find the exact value of cos2x
Answers
Reiny
sketch a right-angled triangle .
since cosØ = 2/5 = x/r
x^2 + y^2 = r^2
4 + y^2 = 25
y^2 = 21
x = ±√21
case 1:
if x = +√21
cosØ = 2/5 , sinØ = √21/5
cos 2Ø = cos^2 Ø- sin^2 Ø
= 4/25 - 21/25 = -17/25
case 2:
if x = - √21/5
cosØ = 2/5, sinØ = -√21/5
but since we are squaring both cosØ and sinØ, we get
cos 2Ø = -17/25
since cosØ = 2/5 = x/r
x^2 + y^2 = r^2
4 + y^2 = 25
y^2 = 21
x = ±√21
case 1:
if x = +√21
cosØ = 2/5 , sinØ = √21/5
cos 2Ø = cos^2 Ø- sin^2 Ø
= 4/25 - 21/25 = -17/25
case 2:
if x = - √21/5
cosØ = 2/5, sinØ = -√21/5
but since we are squaring both cosØ and sinØ, we get
cos 2Ø = -17/25