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Question

The number of real roots of the equation3 sinθ+4 cos θ=6 is
.

A
0.0
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B
2
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C
1
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D
Infinite
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Solution

The correct option is A \N
Here, the equation is of the form a cosθ+b sinθ=c.
Now, dividing the equation by a2+b2=32+42=5 on both sides, we get the equation as:
35 sinθ+45 cosθ=65.
Now, assuming
cosα=45 sinα=35.
Now, we can write the equation as:
cosθcosθ+sinθsinα=65cos(θα)=65>1.
which is not possible as cos θ(1, 1].Thus, the equation has no real roots.

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