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06/01/2022 1:18 pm
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In (sin-1 x )2 - (cos-1 x )2 = a for 0 < x < 1. Then find 2x2 - 1.
(a) sin(2a/π)
(b) cos(4a/π)
(c) cos(2a/π)
(d) sin(4a/π)
1 Answer
1
06/01/2022 1:21 pm
Correct answer: (a) sin(2a/π)
Explanation:
(sin-1 x)2 - (cos-1 x)2 = a
⇒ (sin-1 x)2 - (π/2 - sin-1 x)2 = a
⇒(sin-1 x )2 – (π2/4) - (sin-1 x)2 + π sin-1 x = a
⇒ π sin-1 x = a + π2/4
⇒ x = sin (a/π + π/4)
Now, 2x2 - 1 = 2 sin2(a/π + π/4) - 1
= - cos(2a/π + π/2)
= sin(2a/π)