Is (1+tan^2(x))/(csc(x)sec(x))=tan(x) ?

The answer to whether (1+tan^2(x))/(csc(x)sec(x))=tan(x) is True

Popular >

prove (1+tan^2(x))/(csc(x)sec(x))=tan(x)

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

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

sec (θ) - tan (θ) sin (θ) = \frac{1}{sec ( θ )}

cot (- a) cos (- a) + sin (- a) = - csc (a)

sin (2 a) - tan (a) = tan (a) cos (2 a)

2 cos (x) tan (x) csc (x) = 2

Is (1+tan^2(x))/(csc(x)sec(x))=tan(x) ?
The answer to whether (1+tan^2(x))/(csc(x)sec(x))=tan(x) is True