Question

Solve √3sinx+cosx =2

Answer 1

this question can be solved by auxillary argument

$a \sin(x) + bcos(x) = c$

=

$asinx \: \div { \sqrt{ {a}^{2} + {b}^{2} } } + b\cos(x) \div \\ { \sqrt{ {a}^{2} + {b}^{2} }} \: \\ = c \: \div { \sqrt{ {a}^{2}+ {b}^{2} }}$

$(\sqrt{3} \div 2) \sin(x) + (1 \div 2) \cos(x) = \\ 2 \div 2$

root 3 by two is cos 30

one by two sin 30

$\cos(30) \sin(x) + \sin(30) \cos(x) \\ = 1$

$\sin(30 + x) = \sin(90)$

$n\pi - (\pi \div 6)$

Answer 2

Answer:

Step-by-step explanation: