What is 1/((sin^2(x)+4sin(x)cos(x)+5cos^2(x))) ?

The solution to 1/((sin^2(x)+4sin(x)cos(x)+5cos^2(x))) is 1/(sin^2(x)+2sin(2x)+5cos^2(x))

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simplify 1/((sin^2(x)+4sin(x)cos(x)+5cos^2(x)))

simplify

\frac{1}{( sin ^{2} ( x ) + 4 sin ( x ) cos ( x ) + 5 cos ^{2} ( x ) )}

\frac{1}{sin ^{2} ( x ) + 2 sin ( 2 x ) + 5 cos ^{2} ( x )}

Solution steps

\frac{1}{sin ^{2} ( x ) + 4 sin ( x ) cos ( x ) + 5 cos ^{2} ( x )}

Use the Double Angle identity:

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

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

= 4 \cdot \frac{sin ( 2 x )}{2}

Simplify

4 \cdot \frac{sin ( 2 x )}{2} : 2 sin (2 x)

= \frac{1}{sin ^{2} ( x ) + 2 sin ( 2 x ) + 5 cos ^{2} ( x )}

(x^{2} \cdot y^{- 3})^{- 2}

3 n + \frac{\frac{1}{( 9 \cdot \frac{9 ^{n}}{2} ) ^{1}}}{n} + 2

5 x^{3} - 10 x^{2} + 15

2 (x + 1) (x - 1) - (x - 3) (x + 2)

\frac{d ( t ) 10 x ^{1}}{x + 1}

What is 1/((sin^2(x)+4sin(x)cos(x)+5cos^2(x))) ?
The solution to 1/((sin^2(x)+4sin(x)cos(x)+5cos^2(x))) is 1/(sin^2(x)+2sin(2x)+5cos^2(x))