Write the following trigonometric expression as an algebraic expression containing u and v. Give the restrictions required on u and v. sin ( cos^-1 u sin^-1 v)

--- restriction

Step-by-step explanation:

Given

Required

Write in terms of u and v

Let:

Take arc cos of both sides

Using the following trigonometry identity

So:

Take square roots of both sides

So, we have:

Let:

Take arc cos of both sides

So:

Take square roots

So, we have:

So, we have:

Apply sine rule

Expand

The restriction on u and v is:

asdasd

step-by-step explanation:

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

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