Question

Prove that (sec2A-1)(1-cosec2A)=-1

Answer 1

Step-by-step explanation:

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Answer 2

Proved (sec²A-1)(1-cosec²A) = -1

Given:

(sec²A-1)(1-cosec²A)

To Find:

(sec²A-1)(1-cosec²A) = -1

Solution:

We know the identities,

sec²A - tan²A = 1

⇒ sec²A - 1 = tan²A --- eq1

cosec²A - cot²A = 1

⇒ 1 - cosec²A = -cot²A --- eq2

L.H.S. = (sec²A-1)(1-cosec²A)

Putting values from eq1 and eq2

= (tan²A)(-cot²A)

= (-1) ( tan²A x cot²A)

=(-1) (1) (Since, tanA x cotA = 1)

= -1 (R.H.S)

Hence, proved (sec²A-1)(1-cosec²A) = -1

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