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

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

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prove sin(x)(tan^2(x)+1)=tan(x)sec(x)

prove

sin (x) (tan^{2} (x) + 1) = tan (x) sec (x)

True

Solution steps

sin (x) (tan^{2} (x) + 1) = tan (x) sec (x)

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

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

Manipulating right side

tan (x) sec (x)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

csc (u) = 2

\frac{csc ( x )}{cot ( x )} = csc (x) tan (x)

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

sin (x) + tan (x) = \frac{cos ( x )}{1 - sin ( x )}

1 - \frac{cos ^{2} ( x )}{1 + sin ^{2} ( x )} = sin (s)

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