CBSE Class 10 Answered
If a secA + b tanA+ c =0 and psecA+qsecA+r=0 prove that (br-qc)^2-(pc-ar)^2=(aq-bp)^2
Please answer in a simple way
Asked by guptaabhinav0809 | 10 Feb, 2019, 11:51: PM
Expert Answer
For convenience, let us use the substitutions, sec A = S and tan A = T
given equations are written as :
a×S + b×T = - c ...................(1)
p×S + q×T = - r ...................(2)
by multiplying (1) by p and by multiplying (2) by a, we rewrite the equations as follows
a×p×S + b×p×T = - pc ...........................(3)
a×p×S + q×a×T = - ar ..........................(4)
subtracting (4) from (3), we get, ( b×p - q×a ) T = (ar - pc) or T = tan A = ( pc - ar) / (aq - pb) ............................(5)
Similarly by multiplying (1) by q and by multiplying (2) by b and eliminating T, we get, S = sec A = ( br - cq )/(aq - pb).................(6)
we have, sec2A - tan2A = 1 ..............(7)
by substituting for secA and tanA from (5) and (6) in eqn.(7), it can be shown that, (br-qc)2 - (pc-ar)2 = (aq-pb)2
Answered by Thiyagarajan K | 11 Feb, 2019, 10:41: AM
Application Videos
Concept Videos
CBSE 10 - Maths
Asked by raopaidi | 25 Apr, 2024, 04:06: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by aditikaldate7 | 21 Apr, 2024, 03:16: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by pathaksuman622 | 21 Apr, 2024, 11:56: AM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by yalagondanikhil | 16 Apr, 2024, 12:25: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by rrajansinghakb199 | 08 Apr, 2024, 05:12: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by nagalaxmidurgarao937 | 08 Apr, 2024, 01:42: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by mraniruddha03 | 02 Apr, 2024, 06:44: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by muttenenimalleswarrao | 29 Mar, 2024, 08:32: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by pathakvaishnavi9139 | 23 Mar, 2024, 10:45: AM
ANSWERED BY EXPERT