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Trigonometric Equations

Prove: sec4A...

Question

Prove:
$s e c^{4} A - s e c^{2} A = t a n^{4} A + t a n^{2} A$

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Solution

$s e c^{4} A - s e c^{2} A = s e c^{2} A (s e c^{2} A - 1)$
$= (1 + t a n^{2} A) (1 + t a n^{2} A - 1)$
$= t a n^{2} A + t a n^{4} A$

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Similar questions

Q. Prove that (or prove the identity)

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

Q. 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

prove that inA-cosA+1÷sinA+cosA-1=1÷secA-tanA using identity sec2A = 1+tan2A

Q. (sec⁴ A − sec² A) = ?
(a) tan⁴ A − tan² A
(b) tan² A + tan⁴ A
(c) tan² A − tan⁴ A
(d) None of these

Q. In the following figure,

t a n^{2} A - s e c^{2} A

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