What is the general solution for tan^2(x)cos(x)+cos^2(x)=1 ?

The general solution for tan^2(x)cos(x)+cos^2(x)=1 is x=2pin,x=pi+2pin

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tan^2(x)cos(x)+cos^2(x)=1

tan^{2} (x) cos (x) + cos^{2} (x) = 1

x = 2 πn, x = π + 2 πn

Solution steps

tan^{2} (x) cos (x) + cos^{2} (x) = 1

Subtract

1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sec (x) = 1, sec (x) = - 1

sec (x) = 1 : x = 2 πn

sec (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

sinh (x) = \frac{3}{2}

a = 2 sin (3 0^{\circ} + x) - cos (x)

3 sin^{2} (x) - 6 sin (x) = - 3

tan (\frac{x}{2}) - csc (x) = 0

x, f = e^{s i n (x^{2})}

What is the general solution for tan^2(x)cos(x)+cos^2(x)=1 ?
The general solution for tan^2(x)cos(x)+cos^2(x)=1 is x=2pin,x=pi+2pin