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

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

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simplify (sin(x)+tan(x))^2+cos^2(x)-sec^2(x)

simplify

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

2 sin (x) tan (x)

Solution steps

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

Expand

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

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

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

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

Use the Pythagorean identity:

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

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

= 2 sin (x) tan (x) + 1 - 1

Subtract the numbers:

1 - 1 = 0

= 2 sin (x) tan (x)

(2 x^{2} - 3) ((\frac{1}{x}) + 5)

\frac{3 x + 2}{x ( x ^{2} + 9 )}

\frac{π ( - ln ( 4 + 17 ) + 132 17 )}{256}

- \frac{( 19 + 265 ) k}{8} + 4 k

\frac{( x - 4 ) ^{2}}{4}

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