Prove that

(1 + cot A + tan A) (sin A - cos A) = sin A tan A - cot A cos A

see explanation

Step-by-step explanation:

Using the trigonometric identities

tan A = , cot A =

Consider the left side

(1 + cotA + tanA)(sinA - cosA)

each term in the second factor is multiplied by each term in the first factor.

1(sinA - cosA) + cotA(sinA - cosA) + tanA(sinA - cosA)

= sinA - cosA + cosA - + - sinA ( collect like terms )

= -

= ( sinA × ) - ( × cosA )

= sinAtanA - cotAcosA

= right side ⇒ proven

< 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

⭐dhruv⭐

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.