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Question

The value of a cos θ + b sin θ lies between


A

a-b and a+b

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B

a and b

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C

-(a2+b2) And (a2+b2)

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D

-a2+b2 And a2+b2

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Solution

The correct option is D

-a2+b2 And a2+b2


a cos θ + b sin θ = a2+b2 (acosθa2+b2+bsinθa2+b2)

= a2+b2 sin(θ+ϕ)

Since, 1sin(θ+ϕ) 1,

Then -a2+b2 sin(θ+ϕ) a2+b2.


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