What is expand sec^2(x)+tan(x)(sin(x)-tan(x)) ?

The solution to expand sec^2(x)+tan(x)(sin(x)-tan(x)) is sin(x)tan(x)+1

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expand sec^2(x)+tan(x)(sin(x)-tan(x))

expand

sec^{2} (x) + tan (x) (sin (x) - tan (x))

sin (x) tan (x) + 1

Solution steps

sec^{2} (x) + tan (x) (sin (x) - tan (x))

Expand

tan (x) (sin (x) - tan (x)) : sin (x) tan (x) - tan^{2} (x)

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

Use the Pythagorean identity:

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

sec^{2} (x) - tan^{2} (x) = 1

= sin (x) tan (x) + 1

8 (\frac{3}{2} + 3 x)

\frac{π ( 3 + 3 2 )}{4}

2 (2 + 3)

(2 + 3)^{8}

\frac{2 x}{( x + 1 ) ( x ^{2} + 1 ) ^{2}}

What is expand sec^2(x)+tan(x)(sin(x)-tan(x)) ?
The solution to expand sec^2(x)+tan(x)(sin(x)-tan(x)) is sin(x)tan(x)+1