What is (cos(x)-tan(x))^2+(sin(x)+1)^2 ?

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

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simplify (cos(x)-tan(x))^2+(sin(x)+1)^2

simplify

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

tan^{2} (x) + 2

Solution steps

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

Expand

(cos (x) - tan (x))^{2} : cos^{2} (x) - 2 cos (x) tan (x) + tan^{2} (x)

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

Expand

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

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

Use the Pythagorean identity:

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

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

Add the numbers:

1 + 1 = 2

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

cos (x) tan (x) = sin (x)

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

Add similar elements:

2 sin (x) - 2 sin (x) = 0

= tan^{2} (x) + 2

(3 a - 5 b)^{3}

sin (π) x

n^{3} - n

\frac{a + 2 y}{a - 2 y}

1 - \frac{1}{1 - \frac{1}{2}}

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