Prove that: tan^4A-tan^2A=sec^4A-sec^2A.
Answers
Answered by
3
Answer :
Step By Step Explanation :
tan⁴A - tan²A
✏ tan²A(tan² - 1 )
✏ tan² A ( Sec²A)
✏ (Sec²A - 1 ) (Sec²A)
✏ Sec⁴A - Sec²A
Hence, It's Proved!
Trigonometry Identity Used:
Sec²A = tan²A - 1
Sec²A - tan² A = 1
thanks!
Answered by
5
tan⁴A - tan²A
Step I : Take tan²A Common from Give Equation!
= tan²A(tan²A - 1 )
= tan² A( Sec²A)
[ Note : tan²A - 1 = Sec²A ]
= (Sec²A - 1) Sec²A
= Sec⁴A - Sec² A
Proved!
Trigonometry Identity Used;
Sec²A - tan²A = 1
Sec²A = 1 + tan²A
Sec²A - 1 = tan²A
Step I : Take tan²A Common from Give Equation!
= tan²A(tan²A - 1 )
= tan² A( Sec²A)
[ Note : tan²A - 1 = Sec²A ]
= (Sec²A - 1) Sec²A
= Sec⁴A - Sec² A
Proved!
Trigonometry Identity Used;
Sec²A - tan²A = 1
Sec²A = 1 + tan²A
Sec²A - 1 = tan²A
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