Is tan(x)+2=2+sec(x)sin(x) ?

The answer to whether tan(x)+2=2+sec(x)sin(x) is True

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prove tan(x)+2=2+sec(x)sin(x)

prove

tan (x) + 2 = 2 + sec (x) sin (x)

True

Solution steps

tan (x) + 2 = 2 + sec (x) sin (x)

Manipulating right side

2 + sec (x) sin (x)

Rewrite using trig identities

2 + sec (x) sin (x)

Express with sin, cos

sec (x) sin (x)

Use the basic trigonometric identity:

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

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

Simplify

\frac{1}{cos ( x )} sin (x) : \frac{sin ( x )}{cos ( x )}

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Multiply:

1 \cdot sin (x) = sin (x)

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

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

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

Use the basic trigonometric identity:

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

= 2 + tan (x)

= 2 + tan (x)

= tan (x) + 2

We showed that the two sides could take the same form

\Rightarrow True

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

tan^{2} (α) (1 - sin^{2} (α)) = sin^{2} (α)

\frac{1 - sin ^{2} ( θ )}{sin ^{2} ( θ )} = cot^{2} (θ)

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

sin (θ) \cdot (cot (θ) + tan (θ)) = sec (θ)

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