Is (csc^2(x)-1)(sec^2(x)-1)=1 ?

The answer to whether (csc^2(x)-1)(sec^2(x)-1)=1 is True

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prove (csc^2(x)-1)(sec^2(x)-1)=1

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= cot^{2} (x) tan^{2} (x)

Express with sin, cos

= 1

We showed that the two sides could take the same form

\Rightarrow True

cos (x) + sin (x) \cdot tan (x) = sec (x)

cot (x) + 1 = csc (x) (cos (x) + sin (x))

\frac{csc ( x ) - cot ( x )}{csc ( x )} = 1 - cos (x)

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

sin (θ + \frac{π}{3}) = sin (θ) + sin (\frac{π}{3})

Is (csc^2(x)-1)(sec^2(x)-1)=1 ?
The answer to whether (csc^2(x)-1)(sec^2(x)-1)=1 is True