Is tan(x)*sin(x)+cos(x)=sec(x) ?

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

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prove tan(x)*sin(x)+cos(x)=sec(x)

prove

tan (x) \cdot sin (x) + cos (x) = sec (x)

True

Solution steps

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

Manipulating left side

tan (x) sin (x) + cos (x)

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

sec (x)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{cos ( θ ) + sin ( θ )}{sin ( θ )} = 1 + cot (θ)

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

tan (2 a) - 2 tan (2 a) sin^{2} (a) = sin (2 a)

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

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