JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

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Application +4 | -1

The equation

a\,\,\cos \,\,\theta + b\,\,\sin \,\,\theta = c

has a solution, when

a,\;\,b

and

c

are real numbers such that

View answer and explanation

Correct option: C

{c^2} \le {a^2} + {b^2}

Option C (

{c^2} \le {a^2} + {b^2}

) is correct because the equation

a\cos \theta + b\sin \theta = c

has a solution only if

c

lies within the range

[-\sqrt{a^2+b^2}, \sqrt{a^2+b^2}]

, which implies

{c^2} \le {a^2} + {b^2}

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