Question

if tan theta equals to b by a then a cos 2 theta + b sin 2 theta

Answer 1

tan(x) = sin(x)/cos(x) = b/a

acos(2x) + bsin(2x) =?

Formula:
cos(2x)= 2cos^2(x)-1
sin(2x)=2sin(x)cos(x)

soln:

cos(x) = a , sin(x) = b


2cos^2(x)-1 = 2(a^2)-1
2sin(x)cos(x) = 2ba

acos(2x) + bsin(2x) = 2(a^3)- a + 2ba
=
$a( 2{a}^{2} + b - 1)$