Is sqrt(81-9(3sin(x))^2)=9cos(x) ?

The answer to whether sqrt(81-9(3sin(x))^2)=9cos(x) is False

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prove sqrt(81-9(3sin(x))^2)=9cos(x)

prove

81 - 9 (3 sin (x))^{2} = 9 cos (x)

False

Solution steps

81 - 9 (3 sin (x))^{2} = 9 cos (x)

Show that the two sides are not equal

For

81 - 9 (3 sin (x))^{2} = 9 cos (x)

plug in

x = π

81 - 9 (3 sin (π))^{2} = 9

81 - 9 (3 sin (π))^{2}

Use the following trivial identity:

sin (π) = 0

sin (π)

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= 81 - 9 (3 \cdot 0)^{2}

Simplify

81 - 9 (3 \cdot 0)^{2} : 9

81 - 9 (3 \cdot 0)^{2}

9 (3 \cdot 0)^{2} = 0

9 (3 \cdot 0)^{2}

(3 \cdot 0)^{2} = 0

(3 \cdot 0)^{2}

Apply rule

0 \cdot a = 0

= 0^{2}

Apply rule

0^{a} = 0

= 0

= 9 \cdot 0

Apply rule

0 \cdot a = 0

= 0

= 81 - 0

Subtract the numbers:

81 - 0 = 81

= 81

Factor the number:

81 = 9^{2}

= 9^{2}

Apply radical rule:

9^{2} = 9

= 9

= 9

9 cos (π) = - 9

9 cos (π)

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= (- 1)

= 9 (- 1)

Simplify

= - 9

The two sides are not equal

\Rightarrow False

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

(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)

Is sqrt(81-9(3sin(x))^2)=9cos(x) ?
The answer to whether sqrt(81-9(3sin(x))^2)=9cos(x) is False