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Question

The maximum value of 11111+sinθ1111+cosθ is ___________.

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Solution

Let ∆ = 11111+sinθ1111+cosθ


=11111+sinθ1111+cosθApplying R2R2-R1 and R3R3-R1 =1111-11+sinθ-11-11-11-11+cosθ-1 =1110sinθ000cosθExpanding along C1 =1sinθcosθ =2sinθcosθ2 =sin2θ2 But, sin2θ1sin2θ212

Hence, the maximum value of 11111+sinθ1111+cosθ is 12.

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