Is (1+sec^2(x))/(2+tan^2(x))=1 ?

The answer to whether (1+sec^2(x))/(2+tan^2(x))=1 is True

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prove (1+sec^2(x))/(2+tan^2(x))=1

prove

\frac{1 + sec ^{2} ( x )}{2 + tan ^{2} ( x )} = 1

True

Solution steps

\frac{1 + sec ^{2} ( x )}{2 + tan ^{2} ( x )} = 1

Manipulating left side

\frac{1 + sec ^{2} ( x )}{2 + tan ^{2} ( x )}

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

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

1 + csc^{2} (x) = \frac{1 + sin ^{2} ( x )}{sin ^{2} ( x )}

sec (θ) = cos (θ) + cos (θ) tan^{2} (θ)

\frac{cot ( x ) + csc ( x ) cos ( x )}{cot ( x )} = 2

sec (θ) - cos (θ) = sin (θ) \cdot tan (θ)

Is (1+sec^2(x))/(2+tan^2(x))=1 ?
The answer to whether (1+sec^2(x))/(2+tan^2(x))=1 is True