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

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

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simplify (sqrt(1-cos^2(x)))/(sin(x))+(sqrt(1-sin^2(x)))/(cos(x))

simplify

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

2

Solution steps

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

Least Common Multiplier of

sin (x), cos (x) : sin (x) cos (x)

Adjust Fractions based on the LCM

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

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

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

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

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

Add similar elements:

sin (x) cos (x) + cos (x) sin (x) = 2 sin (x) cos (x)

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

Cancel the common factor:

sin (x)

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

Cancel the common factor:

cos (x)

= 2

(1 + cos (x)) (1 - cos (x))

\frac{3 n}{n + 3} + \frac{5}{n - 4}

\frac{11 - 2}{11 + 2}

\frac{1 + sin ( x )}{cos ( x )}

(2 cos (2 x))^{2}

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