Is 25cos^2(x)=25-25sin^2(x) ?

The answer to whether 25cos^2(x)=25-25sin^2(x) is True

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prove 25cos^2(x)=25-25sin^2(x)

prove

25 cos^{2} (x) = 25 - 25 sin^{2} (x)

True

Solution steps

25 cos^{2} (x) = 25 - 25 sin^{2} (x)

Manipulating right side

25 - 25 sin^{2} (x)

Rewrite using trig identities

25 - 25 sin^{2} (x)

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

sin^{2} (x) = 1 - cos^{2} (x)

= 25 - 25 (1 - cos^{2} (x))

Simplify

25 - 25 (1 - cos^{2} (x)) : 25 cos^{2} (x)

25 - 25 (1 - cos^{2} (x))

Expand

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

- 25 (1 - cos^{2} (x))

Apply the distributive law:

a (b - c) = ab - a c

a = - 25, b = 1, c = cos^{2} (x)

= - 25 \cdot 1 - (- 25) cos^{2} (x)

Apply minus-plus rules

- (- a) = a

= - 25 \cdot 1 + 25 cos^{2} (x)

Multiply the numbers:

25 \cdot 1 = 25

= - 25 + 25 cos^{2} (x)

= 25 - 25 + 25 cos^{2} (x)

25 - 25 = 0

= 25 cos^{2} (x)

= 25 cos^{2} (x)

= 25 cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{1 - sin ( θ )} + \frac{1}{1 + sin ( θ )} = 4 tan (θ)

sin (18 0^{\circ} - θ) = sin (θ)

2 cot^{2} (x) sin^{2} (x) = 1 + 2 cos (x)

\frac{sin ( a )}{1 + cos ( a )} + cot (a) = csc (a)

(cos (x) + sin (x)) 2 = 1 + 2 sin (x) cos (x)

Is 25cos^2(x)=25-25sin^2(x) ?
The answer to whether 25cos^2(x)=25-25sin^2(x) is True