Question

If sin^2+sin^4=1then prove that tan^4-tan^2=1

Answer 1

QUESTION :

If sin^2+sin^4=1then prove that tan^4-tan^2=1

ANSWER :

here

sin²A+sin⁴A=1

so

sin⁴A=1-sin²A

sin⁴A=cos²A.......1

now

LHS

=tan⁴A-tan²A

=(sin⁴A/cos⁴A) - (sin²A/cos²A)

=(cos²A/cos⁴A) - (sin²A/cos²A)

=(1/cos²A) - (sin²A/cos²A)

=(1-sin²A)cos²A

=cos²A/cos²A

=1

=RHS

hence proved

identity used

sin²A+cos²A=1

tanA=(sinA/cosA)