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

The solution to sqrt(-(5sin(x))^2+25) is 5sqrt(cos^2(x))

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simplify sqrt(-(5sin(x))^2+25)

simplify

- (5 sin (x))^{2} + 25

5 cos^{2} (x)

Solution steps

- (5 sin (x))^{2} + 25

Apply exponent rule:

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

= - 5^{2} sin^{2} (x) + 25

Factor

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

= 25 (- sin^{2} (x) + 1)

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 25 - sin^{2} (x) + 1

25 = 5

= 5 - sin^{2} (x) + 1

Rewrite using trig identities

= 5 cos^{2} (x)

sin (\frac{3}{2} π + θ)

\frac{( 1 + tan ^{2} ( x ) )}{se x ( x )}

sin (x - \frac{11 π}{6})

\frac{sin ( - 2 π + θ )}{cos ( 3 π - θ )}

7 cos ((n + 2) π) - 7 cos (nπ)

What is sqrt(-(5sin(x))^2+25) ?
The solution to sqrt(-(5sin(x))^2+25) is 5sqrt(cos^2(x))