Is (1+csc(x))(1+csc(-x))=-cot^4(x) ?

The answer to whether (1+csc(x))(1+csc(-x))=-cot^4(x) is False

Popular >

prove (1+csc(x))(1+csc(-x))=-cot^4(x)

prove

(1 + csc (x)) (1 + csc (- x)) = - cot^{4} (x)

False

Solution steps

(1 + csc (x)) (1 + csc (- x)) = - cot^{4} (x)

Show that the two sides are not equal

For

(1 + csc (x)) (1 + csc (- x)) = - cot^{4} (x)

plug in

x = 1

(1 + csc (1)) (1 + csc (- 1)) = - 0.41228 \dots

(1 + csc (1)) (1 + csc (- 1))

Refine to a decimal form

= - 0.41228 \dots

- cot^{4} (1) = - 0.16997 \dots

- cot^{4} (1)

Refine to a decimal form

= - 0.16997 \dots

The two sides are not equal

\Rightarrow False

1 - \frac{sin ^{2} ( t )}{1 + cos ( t )} = cos (t)

(csc (α) + cot (α)) (sec (α) - 1) = tan (α)

1 - 2 sin^{2} (θ) = 2 cos^{2} (θ) - 1

sin (\frac{π}{4}) = cos (\frac{π}{4})

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

Is (1+csc(x))(1+csc(-x))=-cot^4(x) ?
The answer to whether (1+csc(x))(1+csc(-x))=-cot^4(x) is False