Question

sec⁴ A - sec² A = tan⁴ A + tan² A​

Answer 1

Answer:

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Answer 2

Solution :-

We need to prove ,

sec⁴A - sec²A = tan⁴A + tan²

Firstly taking LHS

→ sec⁴A - sec²A

Simplifying

→ (sec²A)² - sec²A

Substituting sec²A = 1 + tan²A

→ (1 + tan²A)² - (1 + tan²A)

Now , using (a + b)² = a² + b² + 2ab

→ 1² + (tan²A)² + 2(1)(tan²A) - 1 - tan²A

→ 1 + tan⁴A + 2tan²A - 1 - tan²A

→ tan⁴A + 2tan²A - tan²A

→ tan⁴A + tan²A

Now , comparing with RHS

tan⁴A + tan²A = tan⁴A + tan²A

1 = 1

LHS = RHS

Hence , proved !

★ #LearnMore :-

Trigonometric identities

• 1st identity :- sin²A + cos²A = 1

• 2nd identity :- sec²A - tan²A = 1

• 3rd identity :- cosec²A - tan²A = 1