What is the general solution for tan^5(x)tan^2(x)=1 ?

The general solution for tan^5(x)tan^2(x)=1 is x= pi/4+pin

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tan^5(x)tan^2(x)=1

tan^{5} (x) tan^{2} (x) = 1

x = \frac{π}{4} + πn

Solution steps

tan^{5} (x) tan^{2} (x) = 1

Simplify

tan^{5} (x) tan^{2} (x) : tan^{7} (x)

tan^{7} (x) = 1

For

x^{n} = f (a)

, n is odd, the solution is

tan (x) = 1

General solutions for

tan (x) = 1

x = \frac{π}{4} + πn

\frac{sin ^{2} ( a ) + 1}{( 1 + tan ^{2} ( a ) )} = 1

tan (a) = \frac{5}{9}, b = 6

sin^{3} (x) sin^{2} (x) sin (x) = 0

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

sin^{2} (x) cos^{2} (x) = \frac{( 1 - cos ^{4} ( x ) )}{8}

What is the general solution for tan^5(x)tan^2(x)=1 ?
The general solution for tan^5(x)tan^2(x)=1 is x= pi/4+pin