Question

show that tan2A +tan4A=sec4A-sec2A

Answer 1

tan²A+tan⁴A

tan²A(1+tan²A)

(sec²A-1)(1+tan²A). (1+tan²A=sec²A)

(sec²A-1)sec²A

sec⁴A-sec²A  

Answer 2

Answer:

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

Step-by-step explanation:

$LHS = tan^{2} A + tan^{4} A$

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

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

$= ( sec^{2} A - 1 ) \times sec^{2} A$

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

$= RHS$

Therefore.,

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

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