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

tan (θ - 4 5^{\circ}) + tan (θ + 4 5^{\circ}) = 2 tan (2 θ)

tan (2 θ) - tan (θ) = tan (θ) sec (2 θ)

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

tan (2 A) - tan (A) = tan (A) sec (2 A)

\frac{1}{1 - csc ( x )} - \frac{1}{1 + csc ( x )} = - 2 tan (x) sec (x)

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