Question
Download Solution PDFयदि \({\sin ^{ - 1}}x + {\sin ^{ - 1}}y = \frac{\pi }{2}\), तो x2 किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
\(\rm{\sin ^{ - 1}}x + {\cos^{ - 1}}x= \frac{\pi }{2}\)
\(\rm{\sin ^{2}}x + {\cos^{2}}x= 1\)
गणना:
दिया गया है कि \(\rm{\sin ^{ - 1}}x + {\sin ^{ - 1}}y = \frac{\pi }{2}\)
\(\rm{\sin ^{ - 1}}x = \frac{\pi }{2}-{\sin ^{ - 1}}y \)
sin-1 x = cos-1 y
माना x = sin A
sin-1 (sin A) = cos-1 y
A = cos-1 y
y = cos A
y = \(\rm \sqrt{1-\sin^2 A}\)
y2 = 1 - x2
x2 = 1 - y2
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