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

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

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

prove

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

True

Solution steps

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

Manipulating left side

2 tan (x) sec (x) csc (x)

Express with sin, cos

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

Manipulating right side

2 + 2 tan^{2} (x)

Factor

2 + 2 tan^{2} (x) : 2 (1 + tan^{2} (x))

= (1 + tan^{2} (x)) \cdot 2

Express with sin, cos

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{csc ^{2} ( x )}{cot ^{2} ( x )} = csc (x) sec (x)

sin^{2} (b) csc^{2} (b) - sin^{2} (b) = cos^{2} (b)

(tan (θ) + sec (θ)) (1 - sin (θ)) = cos (θ)

cot (π - x) = - cot (x)

sin (θ) cos (θ) + sin^{3} (θ) sec (θ) = tan (θ)

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