Is sin(x)sec^2(x)=(tan(x))/(cos(x)) ?

The answer to whether sin(x)sec^2(x)=(tan(x))/(cos(x)) is True

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prove sin(x)sec^2(x)=(tan(x))/(cos(x))

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

\frac{tan ( x )}{cos ( x )}

We showed that the two sides could take the same form

\Rightarrow True

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

sin (2 θ) = 2 cot (θ) sin^{2} (θ)

tan (θ) + 1 = sec (θ)

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

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

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