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Trigonometry> if asin^(-1)x – bcos^(-1)x=c then a *si...

question mark

if asin^(-1)x – bcos^(-1)x=c then
asin^(-1)x + bcos^(-1)x=????

options are

0

((pi)ab+c(b-a)) /(a+b)

pi/2

[(pi)ab+c(a-b)]/(a+b)

Rohit Falake , 11 Years ago

Grade 12th pass

1 Answers

Jitender Singh

Last Activity: 11 Years ago

$asin^{-1}x-bcos^{-1}x=c$ …............(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

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