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if a*sin^(-1)x – b*cos^(-1)x=c then a *sin^(-1)x + b*cos^(-1)x=???? options are 0 [(pi)ab+c(b-a)]/(a+b) pi/2 [(pi)ab+c(a-b)]/(a+b)

if a*sin^(-1)x – b*cos^(-1)x=c then
a*sin^(-1)x + b*cos^(-1)x=???? 
 
 
options are
  1. 0
  2. [(pi)ab+c(b-a)]/(a+b)
  3. pi/2
  4. [(pi)ab+c(a-b)]/(a+b)

Grade:12th pass

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans: (d)
asin^{-1}x-bcos^{-1}x=c…............(1)
asin^{-1}x+bcos^{-1}x=d…............(2)
We need to find d.
sin^{-1}x+cos^{-1}x=\frac{\pi }{2}
(1)+(2)
\Rightarrow sin^{-1}x = \frac{c+d}{2a}
d = asin^{-1}x+b(\frac{\pi }{2}-sin^{-1}x)
d = (a-b)sin^{-1}x+b\frac{\pi }{2}
d = (a-b)\frac{c+d}{2a}+b\frac{a\pi }{2a}
(a-b)d = +ba\pi(a+b)d = c(a-b)+ba\pi
d = \frac{c(a-b)+ba\pi}{a+b}
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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