Solveeit Logo
Login

Question

Mathematics Question on Trigonometric Equations

The minimum value of 3cosx+4sinx+83cosx + 4sinx + 8 is

A

55

B

99

C

77

D

33

Answer

33

Explanation

Solution

We know that, −32+42≤3 cos x+4 sin x ≤32+42-\sqrt{3^{2}+4^{2}}\le3\,cos\,x+4\,sin\,x\,\le \sqrt{3^{2}+4^{2}} ⇒−25≤3 cosx+4sinx ≤ 25\Rightarrow -\sqrt{25} \le3\,cosx+4sinx \, \le\,\sqrt{25} ⇒−5≤3cosx+4sinx≤5\Rightarrow -5 \le3cosx+4sinx \le 5 ⇒−5+8≤3cosx+4sinx+8≤5+8\Rightarrow -5+8 \le3cosx+4sinx+8 \le 5+8 ⇒3≤3cosx+4sinx+8≤13\Rightarrow 3 \le3cosx+4sinx+8 \le 13 Hence, minimum value of given expression is 33.