What is the general solution for 50sec^2(5x)tan(5x)=25+tan^2(5x) ?

The general solution for 50sec^2(5x)tan(5x)=25+tan^2(5x) is x=(0.40289…)/5+(pin)/5

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50sec^2(5x)tan(5x)=25+tan^2(5x)

50 sec^{2} (5 x) tan (5 x) = 25 + tan^{2} (5 x)

x = \frac{0.40289 \dots}{5} + \frac{πn}{5}

Solution steps

50 sec^{2} (5 x) tan (5 x) = 25 + tan^{2} (5 x)

Subtract

25 + tan^{2} (5 x)

from both sides

50 sec^{2} (5 x) tan (5 x) - 25 - tan^{2} (5 x) = 0

Rewrite using trig identities

- 25 - tan^{2} (5 x) + (1 + tan^{2} (5 x)) \cdot 50 tan (5 x) = 0

Solve by substitution

tan (5 x) \approx 0.42620 \dots

tan (5 x) = 0.42620 \dots : x = \frac{arctan ( 0.42620 \dots )}{5} + \frac{πn}{5}

Combine all the solutions

x = \frac{arctan ( 0.42620 \dots )}{5} + \frac{πn}{5}

Show solutions in decimal form

x = \frac{0.40289 \dots}{5} + \frac{πn}{5}

cot (x) = 8

tan (θ) = \frac{- 1}{6}

sin (3 v) = sin (1 8^{\circ})

tan (x) \cdot sin (x) - 3 sin (x) = 0

sin (θ) = \frac{( - \frac{2}{7} )}{2}

What is the general solution for 50sec^2(5x)tan(5x)=25+tan^2(5x) ?
The general solution for 50sec^2(5x)tan(5x)=25+tan^2(5x) is x=(0.40289…)/5+(pin)/5