Question

tan4A+tan2A=sec4A-sec2A

Answer 1

tan2A(tan2A+1), tan2A=sec2A-1 sec2A-1(sec2A-1+1) sec2A(sec2A-1) sec4A-sec2A Hence proved

Answer 2

Answer:

$tan^{4}A+tan^{2}A=sec^{4}A-sec^{2}A$

Step-by-step explanation:

$tan^{4}A+tan^{2}A\\=tan^{2}A(tan^{2}A+1)\\=(sec^{2}A-1)sec^{2}A$

\* We know the Trigonometric identity:

$\boxed {sec^{2}A=1+tan^{2}A}$

$=sec^{4}A-sec^{2}A\\=RHS$

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