Question
Total number of positive integral value of `n' such that the equations
cos−1x+(sin−1y)2=nπ24 and
(sin−1y)2−cos−1x=π216
are consistent, is equal to :
cos−1x+(sin−1y)2=nπ24 and
(sin−1y)2−cos−1x=π216
are consistent, is equal to :
Answer: Option A
:
A
(sin−1y)2+cos−1x=nπ24
(sin−1y)2−cos−1x=π216
⇒(sin−1y)2=(4n+1)π232,cos−1x=π2(4n−1)32
⇒0≤(4n+1)32π2≤π24,0≤(4n−1)32π2≤π
⇒−14≤n≤74,14,≤n≤8π+14
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:
A
(sin−1y)2+cos−1x=nπ24
(sin−1y)2−cos−1x=π216
⇒(sin−1y)2=(4n+1)π232,cos−1x=π2(4n−1)32
⇒0≤(4n+1)32π2≤π24,0≤(4n−1)32π2≤π
⇒−14≤n≤74,14,≤n≤8π+14
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