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For any acute angle Δ we have,

(i) To prove the first identity


Consider the right triangle ABC, which is right angled at B, then we have p2 + b2 = h2.

Using Pythagoras theorem:

Dividing by h2 we have

But from the above diagram,

Substituting in the above equation, we have

Hence the identity is proved.

(ii) Let us prove the identity

As proved above in the identity (i), we know that

Divide both side of the equation by sin2


Thus the identity is proved.

(iii) Proceeding in the similar manner, let us prove the third identity i.e.

From identity (i) i.e.

Dividing this equation by sin2θ we have,

Hence the identity is proved.


Now let us see few problems where these identities are applied.

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