Is (1+tan^2(θ))/(sec^2(θ))=1 ?

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

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prove (1+tan^2(θ))/(sec^2(θ))=1

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

Simplify

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (A) + cot^{2} (A) cos^{2} (A) = cot^{2} (A)

cot (9 0^{\circ}) = \frac{1}{tan ( 9 0 ^{\circ} )}

sin^{2} (θ) + 9 cos^{2} (θ) + 2 cos (θ) = 2

cot^{2} (y) - cos^{2} (y) = cos^{2} (y) cot^{2} (y)

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

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