Sign of Trigonometric Ratios in Different Quadrants
Suppose, A=...
Question
Suppose, A=dydx of x2+y2=4 at (√2,√2),B=dydx of siny+sinx=sinx⋅siny at (π,π) and C=dydx of 2exy+exey−ex=exy+1 at (1,1), then (A−B−C) has the value equal to .....
A
12
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B
13
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C
1
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D
2
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Solution
The correct option is D12 A:ddx(x2+y2=4) at (√2,√2)) 2x+2ydydx=0 dydx=−xy=−√2√2=−1 B:ddx(siny+sinx=sinx⋅siny) at (π,π) cosydydx+cosx=sinxcosydydx+sinycosx dydx(cosy−sinxcosy)=sinycosx−cosx dydx=cosx(siny−1)cosy(1−sinx) B=−1(0−1)−1(1−0)=−1 C:ddx(2exy+exey−ex=exy+1) at (1,1) [2exy(xdydx+y)]+exeydydx+eyex−ex=exy+1(xdydx+y) dydx=yexy+1−2yexy−ex+y+ex2xexy+ex+y−xexy+1.......... since exey=ex+y C=e2−2e1−e2+e12e1+e2−e2 =−e12e1=−12 Therefore A−B−C=12