Flag Trigonometry> please solve...
question mark

\sqrt{a-b/a+b}=tanAtanB then show that
(a-bCos2A)(a-bCos2B)=a^{2}-b^{2}

Aditya Sharma , 13 Years ago
Grade 12
anser 1 Answers
u. s. p. srinivas aditya

Last Activity: 13 Years ago

sqrt{a-b/a+b}=tanAtanB  (given)

multiplying and dividing (a-b) in LHS...

sqrt{(a-b)(a-b)/(a+b)(a-b)}=tanAtanB

sqrt{(a-b)^2/a^2-b^2}=tanAtanB

squaring both sides...

(a-b)^2/a^2-b^2=tan^2Atan^2B

a^2-b^2=(a-b)^2/tan^2Atan^2B   ~eq.[1]

 

To prove: (a-bCos2A)(a-bCos2B)=a^2-b^2

from eq.[1]

we can prove,  (a-b)^2/tan^2Atan^2B=(a-bCos2A)(a-bCos2B)

RHS-

=> {a-b[(1-tan^2A)/(1+tan^2A)]}{a-b[(1-tan^2B)/(1+tan^2B)]} 

=> [a-(b-btan^2A)/(1+tan^2A)][a-(b-btan^2B)/(1+tan^2B)]

=> [(a+atan^2A-b+btan^2A)(a+atan^2B-b+btan^2B)]/[1+tan^2A+tan^2B+tan^2Atan^2B]

on solving further....

=> (a^2+b^2-2ab)(tan^2B)/(tan^2Atan^4B)

=> (a-b)^2/tan^2Atan^2B

                          hence proved...!! 

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