Is 1+sec^2(x)*sin^2(x)=sec^2(x) ?

The answer to whether 1+sec^2(x)*sin^2(x)=sec^2(x) is True

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prove 1+sec^2(x)*sin^2(x)=sec^2(x)

prove

1 + sec^{2} (x) \cdot sin^{2} (x) = sec^{2} (x)

True

Solution steps

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

Manipulating left side

1 + sec^{2} (x) sin^{2} (x)

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

sec^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (a) + sin^{2} (a) = 1

sin (x) cos (x) = sin (x)

cos (3 x) = cos (x) (cos^{2} (x) - 3 sin^{2} (x))

(sec (x) - 1) (sec (x) + 1) \cdot cot^{2} (x) = 1

csc (x) sin (\frac{π}{2} - x) = cot (x)

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