What is sqrt(25sec^2(5x)-25) ?

The solution to sqrt(25sec^2(5x)-25) is 5tan(5x)

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simplify sqrt(25sec^2(5x)-25)

simplify

25 sec^{2} (5 x) - 25

5 tan (5 x)

Solution steps

25 sec^{2} (5 x) - 25

Factor

25 sec^{2} (5 x) - 25 : 25 (sec^{2} (5 x) - 1)

= 25 (sec^{2} (5 x) - 1)

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 25 sec^{2} (5 x) - 1

25 = 5

= 5 sec^{2} (5 x) - 1

Use the Pythagorean identity:

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

sec^{2} (x) - 1 = tan^{2} (x)

= 5 tan^{2} (5 x)

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

= 5 tan (5 x)

sec (arctan (6 x))

cos (arcsin (\frac{y}{x}))

sin (\frac{3 π}{10} (- x))

cos (4 5^{\circ} + θ)

cos (- π t + π)