Is 8-4csc^2(z)=4-4cot^2(z) ?

The answer to whether 8-4csc^2(z)=4-4cot^2(z) is True

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prove 8-4csc^2(z)=4-4cot^2(z)

prove

8 - 4 csc^{2} (z) = 4 - 4 cot^{2} (z)

True

Solution steps

8 - 4 csc^{2} (z) = 4 - 4 cot^{2} (z)

Manipulating left side

8 - 4 csc^{2} (z)

Rewrite using trig identities

8 - 4 csc^{2} (z)

Use the Pythagorean identity:

csc^{2} (x) = 1 + cot^{2} (x)

= 8 - 4 (1 + cot^{2} (z))

Simplify

8 - 4 (1 + cot^{2} (z)) : - 4 cot^{2} (z) + 4

8 - 4 (1 + cot^{2} (z))

Expand

- 4 (1 + cot^{2} (z)) : - 4 - 4 cot^{2} (z)

- 4 (1 + cot^{2} (z))

Apply the distributive law:

a (b + c) = ab + a c

a = - 4, b = 1, c = cot^{2} (z)

= - 4 \cdot 1 + (- 4) cot^{2} (z)

Apply minus-plus rules

+ (- a) = - a

= - 4 \cdot 1 - 4 cot^{2} (z)

Multiply the numbers:

4 \cdot 1 = 4

= - 4 - 4 cot^{2} (z)

= 8 - 4 - 4 cot^{2} (z)

Subtract the numbers:

8 - 4 = 4

= - 4 cot^{2} (z) + 4

= - 4 cot^{2} (z) + 4

= - 4 cot^{2} (z) + 4

= 4 - 4 cot^{2} (z)

We showed that the two sides could take the same form

\Rightarrow True

p ro v e 3 sec^{2} (x) - 2 tan^{2} (x) - 4 = 0

p ro v e tan (θ) cot (θ) - 1 = 1 - sec (θ) cos (θ)

p ro v e \frac{cot ( 2 x )}{cos ( 2 x )} = csc (2 x)

p ro v e tan (\frac{7 π}{6}) = \frac{3}{3}

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

Is 8-4csc^2(z)=4-4cot^2(z) ?
The answer to whether 8-4csc^2(z)=4-4cot^2(z) is True