Question

If cos⁴A+cos²A=1,prove that tan⁴A+tan²A=1​

Answer 1

hope this helps u

QUESTION :

tan⁴A +tan²A=1

then show that cos⁴ A+cos²A=1

ANSWER :

Here

tan⁴A+tan²A=1

tan⁴A=1-tan²A

tan⁴A=sec²A

sin⁴A/cos⁴A =1/cos²A

sin⁴A=cos²A

so by taking square root on both the sides

√sin⁴A=√cos²A

sin²A=cosA........1

now

LHS

=cos⁴A +cos²A

sin²A+cos²A.....from 1

=1

=RHS

identity used :

sin²A+cos²A=1

tanA=sinA/cosA

1+tan²A=sec²A

Answer 2

Answer:

tan⁴A +tan²A=1

then show that cos⁴ A+cos²A=1

ANSWER :

Here

tan⁴A+tan²A=1

tan⁴A=1-tan²A

tan⁴A=sec²A

sin⁴A/cos⁴A =1/cos²A

sin⁴A=cos²A

so by taking square root on both the sides

√sin⁴A=√cos²A

sin²A=cosA........1

now

LHS

=cos⁴A +cos²A

sin²A+cos²A.....from 1

=1

=RHS

identity used :

sin²A+cos²A=1

tanA=sinA/cosA

1+tan²A=sec²A