Is 7csc^2(θ)-5cot^2(θ)=2csc^2(θ)+5 ?

The answer to whether 7csc^2(θ)-5cot^2(θ)=2csc^2(θ)+5 is True

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prove 7csc^2(θ)-5cot^2(θ)=2csc^2(θ)+5

prove

7 csc^{2} (θ) - 5 cot^{2} (θ) = 2 csc^{2} (θ) + 5

True

Solution steps

7 csc^{2} (θ) - 5 cot^{2} (θ) = 2 csc^{2} (θ) + 5

Manipulating left side

7 csc^{2} (θ) - 5 cot^{2} (θ)

Rewrite using trig identities

= 2 csc^{2} (θ) + 5

We showed that the two sides could take the same form

\Rightarrow True

cos (θ) = \frac{cot ( θ )}{csc ( θ )}

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

cos (x - \frac{3 π}{2}) = - sin (x)

\frac{sec ^{2} ( x )}{2 - sec ^{2} ( x )} = sec (2 x)

\frac{cot ( x ) tan ( x )}{cos ( x )} = sec (x)

Is 7csc^2(θ)-5cot^2(θ)=2csc^2(θ)+5 ?
The answer to whether 7csc^2(θ)-5cot^2(θ)=2csc^2(θ)+5 is True