Is 8csc^2(x)-3cot^2(x)=3+5csc^2(x) ?

The answer to whether 8csc^2(x)-3cot^2(x)=3+5csc^2(x) is True

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prove 8csc^2(x)-3cot^2(x)=3+5csc^2(x)

prove

8 csc^{2} (x) - 3 cot^{2} (x) = 3 + 5 csc^{2} (x)

True

Solution steps

8 csc^{2} (x) - 3 cot^{2} (x) = 3 + 5 csc^{2} (x)

Manipulating left side

8 csc^{2} (x) - 3 cot^{2} (x)

Rewrite using trig identities

8 csc^{2} (x) - 3 cot^{2} (x)

Use the Pythagorean identity:

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

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

= 8 csc^{2} (x) - 3 (csc^{2} (x) - 1)

Simplify

8 csc^{2} (x) - 3 (csc^{2} (x) - 1) : 5 csc^{2} (x) + 3

8 csc^{2} (x) - 3 (csc^{2} (x) - 1)

Expand

- 3 (csc^{2} (x) - 1) : - 3 csc^{2} (x) + 3

- 3 (csc^{2} (x) - 1)

Apply the distributive law:

a (b - c) = ab - a c

a = - 3, b = csc^{2} (x), c = 1

= - 3 csc^{2} (x) - (- 3) \cdot 1

Apply minus-plus rules

- (- a) = a

= - 3 csc^{2} (x) + 3 \cdot 1

Multiply the numbers:

3 \cdot 1 = 3

= - 3 csc^{2} (x) + 3

= 8 csc^{2} (x) - 3 csc^{2} (x) + 3

Add similar elements:

8 csc^{2} (x) - 3 csc^{2} (x) = 5 csc^{2} (x)

= 5 csc^{2} (x) + 3

= 5 csc^{2} (x) + 3

= 5 csc^{2} (x) + 3

= 3 + 5 csc^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (t) = (sin (t))^{2}

sin (2 x) - 2 cos (x) = 0, (0, 2 π)

sin (\frac{( 5 π )}{3})

sin (\frac{( 5 π )}{2})

sin (\frac{( 3 π )}{2})

Is 8csc^2(x)-3cot^2(x)=3+5csc^2(x) ?
The answer to whether 8csc^2(x)-3cot^2(x)=3+5csc^2(x) is True