Question

"Question47
Prove the identity : (sec² θ -1) (cosec² θ -1) = 1
Chapter7,Trigonometric identities Exercise -7A , Page number 314"

Answer 1

Hey there!

We will prove this by using identities.

We know that,

sec²A - tan²A = 1
sec²A - 1 = tan²A

Also, cosec²A - cot²A = 1
cosec²A - 1 = cot²A

And tanA * cotA = 1

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Coming back to your question,

L. H. S


= (sec² θ - 1) ( cosec²θ - 1 )

= tan² θ * cot² θ

= ( tan θ * cot θ ) ²

= 1²

= 1



= R. H. S

Hence, (sec² θ - 1) ( cosec²θ- 1 ) = 1

In this type of questions, we need to decide choose identity helps us. Trigonometry is simple and you can do it by understanding things well. This question will seem confusing if you write different identities .We could also have proved it by other means , But I proved it this way as it is of Trigonometric identities chapter.

$\therefore$ We proved (sec² θ - 1) (cosec² θ -1 ) = 1

Answer 2

Heya user☺☺

Hope this will help☺☺