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Question

The number of values of θ satisfying 4cosθ+3sinθ=5 as well as 3cosθ+4sinθ=5 is

A
1
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B
2
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C
0
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D
None of these
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Solution

The correct option is C 0
4cosθ+3sinθ=5 and 3cosθ+4sinθ=5
45cosθ+35sinθ=1
Let sinA=45cosA=35
sinAcosθ+cosAsinθ=1
sin(A+θ)=1
A+θ=π2.....(1)
Now second equation 3cosθ+4sinθ=5
35cosθ+45sinθ=1
cosAcosθ+sinAsinθ=1
cos(θA)=1
θA=0
θ=A
2θ=π2 ........ From (1)
θ=π4
Put value of θ in 4cosθ+3sinθ=5
LHS= 4cosπ4+3sinπ4=42+32=725
No solution exists
No. of solutions =0

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