What is the general solution for 4cos(x)=sec(x) ?

The general solution for 4cos(x)=sec(x) is x= pi/3+2pin,x=(5pi)/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

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4cos(x)=sec(x)

4 cos (x) = sec (x)

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

4 cos (x) = sec (x)

Subtract

sec (x)

from both sides

4 cos (x) - sec (x) = 0

Rewrite using trig identities

\frac{4}{sec ( x )} - sec (x) = 0

Solve by substitution

sec (x) = 2, sec (x) = - 2

sec (x) = 2 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sec (x) = - 2 : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

9.6 = 11.6 cos (3.922 t)

2 sin^{2} (x) = tan^{2} (x)

cos (θ) = 0.5632

sin (z) = - 10

\frac{sec ^{2} ( A ) + cot ^{2} ( A )}{csc ^{2} ( A )} = sec^{2} (A)

What is the general solution for 4cos(x)=sec(x) ?
The general solution for 4cos(x)=sec(x) is x= pi/3+2pin,x=(5pi)/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin