Question

"Question45
Prove the identity : (1 + cot² θ ) sin² θ = 1
Chapter7,Trigonometric identities Exercise -7A , Page number 314"

Answer 1

Hey there!

We will prove this by using identities.

We know that,

cosec²A - cot²A = 1

Now,

1 + cot²A = cosec²A.

Also, sinA = 1/ cosecA .

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Coming back to your question,

L. H. S

= (1 + cot² θ ) sin² θ

= cosec²θ ( sin²θ )

= [ cosecθ . sinθ ] ²

= 1²

= 1 .

= R. H. S

Hence, (1 + cot² θ ) sin² θ = 1

In this type of questions, First we need to decide which 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 (1 + cot² θ ) sin² θ = 1

Answer 2

1+cot^2thita=cosec^2thita
cosec^2thita×sin^2thita
1/sin^2thita×sin^2thita=1=rhs
is your answer