Is 25tan^2(5x)+25=25+(5tan(5x))^2 ?

The answer to whether 25tan^2(5x)+25=25+(5tan(5x))^2 is True

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prove 25tan^2(5x)+25=25+(5tan(5x))^2

prove

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

True

Solution steps

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

Manipulating right side

25 + (5 tan (5 x))^{2}

Simplify

(5 tan (5 x))^{2} + 25 : 25 tan^{2} (5 x) + 25

(5 tan (5 x))^{2} + 25

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

5^{2} = 25

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

(1 + tan (a)) \cdot (1 - tan (a)) = 2 - sec^{2} (a)

(cot (x)) (sec (x)) (sin (x)) = 1

\frac{cos ^{2} ( x ) - 4}{cos ( x ) - 2} = cos (x) + 2

sin^{2} (a) tan^{2} (a) = tan^{2} (a) - sin^{2} (a)

\frac{cos ( a )}{1 - sin ( a )} - tan (a) = sec (a)

Is 25tan^2(5x)+25=25+(5tan(5x))^2 ?
The answer to whether 25tan^2(5x)+25=25+(5tan(5x))^2 is True