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

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

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

simplify

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

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

Solution steps

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

Expand

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

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

Expand

(1 - cos (x))^{2} : 1 - 2 cos (x) + cos^{2} (x)

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

Use the Pythagorean identity:

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

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

Add the numbers:

1 + 1 = 2

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

sin (0)

3 cos (π (x - 1))

2 ((4, 0, - 3, 5) + 3 (0, 2, 5, 4))

(9 x + 8) (8 x - \frac{1}{2})

\frac{( x ^{2} - 1 ) ^{2}}{4 x ^{2}}

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