joshuanozawa
joshuanozawa
11-03-2021
Mathematics
contestada
prove tan2 x sin2 x = tan2 x − sin2 x
Respuesta :
Nayefx
Nayefx
11-03-2021
Answer:
SEE BELOW
Step-by-step explanation:
to understand this
you need to know about:
trigonometry
PEMDAS
tips and formulas:
tanA=sinA/cosA
sin²A=1-cos²A
let's solve:
L.H.S=
[tex] \sf rewrite \: \tan ^{2} (x) \: as \: \frac{sin ^{2}(x) }{ \cos ^{2} (x) } : \\ \sf \sin^{2} (x). (\frac{sin ^{2}(x) }{ \cos ^{2} (x) }) [/tex]
[tex] \sf rewrite \: si {n}^{2} x \: as \: 1 - co {s}^{2} x : \\ \sf \sin^{2} (x). \{\frac{1 - cos ^{2}(x) }{ {cos}^{2}(x) } \}[/tex]
[tex] \sf \: rewrite: \\ \sf \sin^{2} (x). \{\frac{1 }{ {cos}^{2}(x) } - 1\}[/tex]
[tex] \sf distribute : \\ \frac{ \sin ^{2} (x) }{ \cos ^{2} (x) } - \sin ^{2} (x) \\ \tan ^{2} (x) - \sin ^{2} (x) [/tex]
=R.H.S
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