Is sec^2(Θ)csc^2(Θ)=sec^2(Θ)+csc^2(Θ) ?

The answer to whether sec^2(Θ)csc^2(Θ)=sec^2(Θ)+csc^2(Θ) is True

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prove sec^2(Θ)csc^2(Θ)=sec^2(Θ)+csc^2(Θ)

prove

sec^{2} (Θ) csc^{2} (Θ) = sec^{2} (Θ) + csc^{2} (Θ)

True

Solution steps

sec^{2} (Θ) csc^{2} (Θ) = sec^{2} (Θ) + csc^{2} (Θ)

Manipulating right side

sec^{2} (Θ) + csc^{2} (Θ)

Express with sin, cos

= \frac{cos ^{2} ( Θ ) + sin ^{2} ( Θ )}{cos ^{2} ( Θ ) sin ^{2} ( Θ )}

Rewrite using trig identities

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

Rewrite using trig identities

sec^{2} (Θ) csc^{2} (Θ)

We showed that the two sides could take the same form

\Rightarrow True

\frac{cos ( t )}{1 - sin ( t )} = sec (t) + tan (t)

(sec (x) - 1)^{4} = 2 tan^{2} (x) - tan^{4} (x)

sin (2 x) = 2 \frac{cos ( x )}{csc ( x )}

2 sin (3 0^{\circ}) cos (3 0^{\circ}) = sin (6 0^{\circ})

\frac{cot ( θ ) + tan ( θ )}{cot ( θ )} = sec^{2} (θ)

Is sec^2(Θ)csc^2(Θ)=sec^2(Θ)+csc^2(Θ) ?
The answer to whether sec^2(Θ)csc^2(Θ)=sec^2(Θ)+csc^2(Θ) is True