Is cos(t)+tan(t)sin(t)=sec(t) ?

The answer to whether cos(t)+tan(t)sin(t)=sec(t) is True

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prove cos(t)+tan(t)sin(t)=sec(t)

prove

cos (t) + tan (t) sin (t) = sec (t)

True

Solution steps

cos (t) + tan (t) sin (t) = sec (t)

Manipulating left side

cos (t) + tan (t) sin (t)

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{cos ( t )}

Rewrite using trig identities

sec (t)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 - cos ( x )}{- 1 + \frac{1}{c o s ( x )}} = cos (x)

cos^{4} (x) - sin^{4} (x) = tan^{2} (x)

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

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

tan^{3} (x) = \frac{sin ^{3} ( x )}{cos ^{3} ( x )}

Is cos(t)+tan(t)sin(t)=sec(t) ?
The answer to whether cos(t)+tan(t)sin(t)=sec(t) is True