Is sqrt(81-9(3sin(x))^2)=sec^4(x) ?

The answer to whether sqrt(81-9(3sin(x))^2)=sec^4(x) is False

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prove sqrt(81-9(3sin(x))^2)=sec^4(x)

prove

81 - 9 (3 sin (x))^{2} = sec^{4} (x)

False

Solution steps

81 - 9 (3 sin (x))^{2} = sec^{4} (x)

Show that the two sides are not equal

For

81 - 9 (3 sin (x))^{2} = sec^{4} (x)

plug in

x = 0

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

81 - 9 (3 sin (0))^{2}

Use the following trivial identity:

sin (0) = 0

sin (0)

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

sec^{4} (0) = 1

sec^{4} (0)

Use the following trivial identity:

sec (0) = 1

sec (0)

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 1

= 1^{4}

Simplify

= 1

The two sides are not equal

\Rightarrow False

sin (4 0^{\circ}) = 2 sin (2 0^{\circ}) cos (2 0^{\circ})

sin (θ) - cos^{2} (θ) sin (θ) = sin^{3} (θ)

\frac{9}{sec ( x ) + 1} - \frac{9}{sec ( x ) - 1} = 0

sec^{2} (x) + csc^{2} (x) = (sec (x) csc (x))^{2}

tan (x) = \frac{sin ( x ) csc ( x )}{cot ( x )}

Is sqrt(81-9(3sin(x))^2)=sec^4(x) ?
The answer to whether sqrt(81-9(3sin(x))^2)=sec^4(x) is False