The equation a text cos θ +b text sin θ =c has a solution, when a , b and c are real numbers such that:

Question

The equation a text cos θ +b text sin θ =c has a solution, when a , b and c are real numbers such that: (A)  a < b < c  (B)  a=b=c  (C)  c2 le a2+b2  (D)  c2<a2-b2

Tardigrade Admin · Accepted Answer

The given equation is a text cosθ +b text sinθ =c Since, √a2-b2 le a cos θ +b sin θ le √a2+b2 ⇒ c2 le √a2+b2

Q. The equation $a cos θ + b s in θ = c$ has a solution, when $a$ , $b$ and $c$ are real numbers such that:

$a < b < c$

$a = b = c$

$c^{2} \leq a^{2} + b^{2}$

$c^{2} < a^{2} - b^{2}$

for all real values of a, b and c

The given equation is
$a cos θ + b s in θ = c$
Since, $a^{2} - b^{2} \leq a cos θ + b sin θ \leq a^{2} + b^{2}$
$\Rightarrow$ $c^{2} \leq a^{2} + b^{2}$

Q. The equation acosθ+bsinθ=c has a solution, when a , b and c are real numbers such that:

a<b<c

a=b=c

c2≤a2+b2

c2<a2−b2