Is 9sec^2(θ)-5tan^2(θ)=5+4sec^2(θ) ?

The answer to whether 9sec^2(θ)-5tan^2(θ)=5+4sec^2(θ) is True

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prove 9sec^2(θ)-5tan^2(θ)=5+4sec^2(θ)

prove

9 sec^{2} (θ) - 5 tan^{2} (θ) = 5 + 4 sec^{2} (θ)

True

Solution steps

9 sec^{2} (θ) - 5 tan^{2} (θ) = 5 + 4 sec^{2} (θ)

Manipulating left side

9 sec^{2} (θ) - 5 tan^{2} (θ)

Rewrite using trig identities

= 4 sec^{2} (θ) + 5

= 5 + 4 sec^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

cot (2 θ) = cot (θ) - \frac{1}{2} sec (θ) csc (θ)

(csc (x) - cot (x)) (csc (x) + cot (x)) = 1

(tan (x)) (sin (x)) = sec (x) - cos (x)

tan (α) + cot (α) = sec (α) csc (α)

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

Is 9sec^2(θ)-5tan^2(θ)=5+4sec^2(θ) ?
The answer to whether 9sec^2(θ)-5tan^2(θ)=5+4sec^2(θ) is True