Q. 53.5( 4 Votes )
sec4 A − sec2 A is equal to
A. tan2 A − tan4 A
B. tan4 A − tan2 A
C. tan4 A + tan2 A
D. tan2 A + tan4 A
Answer :
Note: Since all the options involve the trigonometric ratio tan θ, so we use the identity 1 + tan2 θ = sec2 θ.
To find: sec4 A – sec2 A
Consider sec4 A – sec2 A = (sec2 A)2 – sec2 A
Now, as sec2 A = 1 + tan2 A
⇒ sec4 A – sec2 A = (sec2 A)2 – sec2 A
= (1 + tan2 A)2 – (1 + tan2 A)
= 1 + tan4 A + 2 tan2 A – 1 – tan2 A
= tan4 A + tan2 A
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