Is csc^2(x)+1=cot^2(x)+2 ?

The answer to whether csc^2(x)+1=cot^2(x)+2 is True

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prove csc^2(x)+1=cot^2(x)+2

prove

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

True

Solution steps

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

Manipulating right side

cot^{2} (x) + 2

Rewrite using trig identities

cot^{2} (x) + 2

Use the Pythagorean identity:

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

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

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

Simplify

= csc^{2} (x) + 1

= csc^{2} (x) + 1

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (a) = 1 - cos^{2} (a)

\frac{sin ( x )}{cot ^{2} ( x )} = \frac{tan ^{2} ( x )}{csc ( x )}

sin (x) \cdot (1 + cot (x)) = sin (x) + cos (x)

sin (\frac{5 π}{4}) = cos (\frac{5 π}{4})

2 sin^{2} (x) - cos^{2} (x) (tan^{2} (x) - 1) = 1