Question

Prove that (sec^4 - sec^2) = tan^2 + tan^4

Answer 1

Answer:

sec^4 A - sec^2 A = tan^2 + tan^4 A

Step-by-step explanation:

From the properties of trigonometry :

• 1 + tan^2 A = sec^2 A
• So, sec^2 A - 1 = tan^2 A

Here,

⇒ sec^4 A - sec^2 A

⇒ sec^2 A ( sec^2 - 1 )

⇒ sec^2 A( tan^2 )              { sec^2 A - 1 = tan^2 A }

⇒ ( 1 + tan^2 A )( tan^2 A )     { sec^2 A = 1 + tan^2 A }

⇒ tan^2 A + tan^4

Proved.