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Popular >

cos(2x)=sec(x)

Solution

cos (2 x) = sec (x)

Solution

x = 2 πn

+1

Solution steps

cos (2 x) = sec (x)

Subtract

sec (x)

from both sides

cos (2 x) - sec (x) = 0

Rewrite using trig identities

- 1 - \frac{1}{cos ( x )} + 2 cos^{2} (x) = 0

Solve by substitution

cos (x) = 1, cos (x) = - \frac{1}{2} + i \frac{1}{2}, cos (x) = - \frac{1}{2} - i \frac{1}{2}

cos (x) = 1 : x = 2 πn

cos (x) = - \frac{1}{2} + i \frac{1}{2} :

No Solution

cos (x) = - \frac{1}{2} - i \frac{1}{2} :

No Solution

Combine all the solutions

x = 2 πn

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7^{s i n (θ) + 1 - 3 s i n^{2} (θ)} = (\frac{1}{7})^{s i n^{2} (θ)}

14sin(x+pi/2)+21tan(pi-x)=0

14 sin (x + \frac{π}{2}) + 21 tan (π - x) = 0

tan (x) = - \frac{15}{8}

8cos^3(x)=8cos(x)

8 cos^{3} (x) = 8 cos (x)

Frequently Asked Questions (FAQ)

What is the general solution for cos(2x)=sec(x) ?
The general solution for cos(2x)=sec(x) is x=2pin