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Question

The value of sin θ+cos θ will be greatest when


A

θ=30

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B

θ=45

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C

θ=60

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D

θ=90

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Solution

The correct option is B

θ=45


Let f(x)=sin θ+cos θ=2sin(θ+π4)But1sin(θ+π2)122sin(θ+π4)2.

Hence the maximum value of (sin θ+cos θ)

i.e., of 2 sin(θ+π4)=2. sin(θ+π4)=1 sin(θ+π4)=sin π2θ+π4=π2θ=π4=45


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