Prove that cos A / (1 + sin A) + tan A = sec A.

Market valueof eachshare= = ₹32

1. (a)

cosA Left-hand side. = + tanA 1 + sinA cos A(1 sinA) sinA (1 sinA)(1 sinA) cosA cosA sinAcosA sinA cosA 1 sin A cosA sinAcosA sinA = cosA cos A 1 sinA sinA = cosA cosA cosA = cosA = secA = Right-hand side

(b) (i) Steps of construction:

1. Draw BC=6.5cmusing a ruler.
2. WithBas thecentreandradiusequal toapproximately half of BC,

draw anarc that cuts thesegment BCat Q.

1. WithQ as thecentre,andsameradius,cut thepreviousarcat P.
2. JoinBPandextendit.
3. WithBas thecentreandradius5cm, draw anarc that cuts the

armPBtoobtain point A.

1. Join AC toobtain ΔABC.

(ii)Stepsforconstruction :

1. With Aas thecentreandradius3.5cm,draw acircle.
2. Thecircumferenceof acircleis therequiredlocus.

(iii)Stepsforconstruction :

1. WithCas thecentreand withradiusof a lengthless than CA orBC,

draw anarc tocut the linesegments ACandBCat DandErespectively.

1. With thesameradiusorasuitableradiusand withDas thecentre,

draw anarcof acircle.

1. With thesameradiusand withEas thecentredraw anarcsuch that

thetwoarcsintersect at H.

1. JoinCandH.
2. CHis thebisectorof ÐACBandis therequiredlocus.

(iv) Stepsforconstruction:

1. Weknown that thepointsat a distanceof 3.5cmfrom A will

surely lieon thecircle withcentre A.

1. Also, thepointson theanglebisectorCHare thepoints equidistant from

ACandBC.

1. Mark X and Y whichareat theintersectionof thecircleand theangle

bisectorCH.

1. Measure XY. XY=5cm

(c) (i) Total dividend = ₹2,475 Dividend on each share 12% of ₹25= 25 ₹3 Total dividend 2475 Number of shares bought 825 Dividend on 1 share 3 ≤ ∴ TotalInvestment 26400 (ii) Market valueof eachshare= = ₹32 Numberof sharesbought 825