Question

Prove tan2 x sin2 x = tan2 x − sin2 x​

Answer 1

SEE BELOW

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=

1. 
   `\sf rewrite \: \tan ^(2) (x) \: as \: (sin ^(2)(x) )/( \cos ^(2) (x) ) : \\ \sf \sin^(2) (x). ((sin ^(2)(x) )/( \cos ^(2) (x) ))`
2. 
   `\sf rewrite \: si {n}^(2) x \: as \: 1 - co {s}^(2) x : \\ \sf \sin^(2) (x). \{\frac{1 - cos ^(2)(x) }{ {cos}^(2)(x) } \}`
3. 
   `\sf \: rewrite: \\ \sf \sin^(2) (x). \{\frac{1 }{ {cos}^(2)(x) } - 1\}`
4. 
   `\sf distribute : \\ ( \sin ^(2) (x) )/( \cos ^(2) (x) ) - \sin ^(2) (x) \\ \tan ^(2) (x) - \sin ^(2) (x)`

=R.H.S