Flag Trigonometry> If tan teta+sinteta=m,tanteta=m,tanteta-s...
question mark

If tan teta+sinteta=m,tanteta=m,tanteta-sinteta=n and m is not equal n then prove that m2-n2=4rootmn

Nandan gowda , 6 Years ago
Grade 10
anser 1 Answers
Arun

Last Activity: 6 Years ago

Given :- (1)  TanA + SinA = m

  (2)  TanA - SinA = n

To prove :- m2 - n2 = 4  x  (root mn)

 

Proof :-

L.H.S =  m2 - n2

  = (TanA + SinA)2 - (TanA - SinA)2

  = (Tan2A + Sin2A + 2 TanA SinA) - ( Tan2A + Sin2A - 2 TanA SinA)

  = Tan2A + Sin2A + 2 TanA SinA - Tan2A - Sin2A + 2 TanA SinA

  = Tan2+ Sin2+ 2 TanA SinA - Tan2A  - Sin2A + 2 TanA SinA

  = 4 TanA SinA

R..H.S ;- 4 root mn

  = 4 x [ root (TanA + SinA)(TanA - SinA) ]

  = 4 x [ root ( Tan2A - Sin2A ) ]

  = 4 x [ root ( Sin2A / Cos2A  -  Sin2A )

  = 4 x [ root { (Sin2A - Sin2ACos2A) / Cos2A } ]

  = 4 x [ root { Sin2A (1 - Cos2A) } / Cos2A ]

  = 4 x [ root { (Sin2A  x  Sin2A ) / Cos2A ]

  = 4 x (root [ Sin2A Tan2A ] )

  = 4 TanA SinA = L.H.S

 

Hence Proved

Provide a better Answer & Earn Cool Goodies

Enter text here...
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Enter text here...