Is 25(sec^2(5x)-tan^2(5x))=25 ?

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

prove 25(sec^2(5x)-tan^2(5x))=25

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

= 25 \cdot 1

Simplify

= 25

= 25

We showed that the two sides could take the same form

\Rightarrow True

p ro v e cot^{2} (x) = \frac{( cos ^{2} ( x ) )}{1 - cos ^{2} ( x )}

p ro v e + \frac{cos ( x )}{1 - sin ( x )} = sec (x) + tan (x)

p ro v e sin (\frac{4 π}{3}) = 3 cos (\frac{2 π}{3})

p ro v e sin^{2} (x) + sin^{2} (θ) = 1

p ro v e \frac{cot ( x ) - sec ( x )}{csc ( x )} = 1

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