What is expand (sin((3t)/2)+cos((3t)/2))^2 ?

The solution to expand (sin((3t)/2)+cos((3t)/2))^2 is sin(2*(3t)/2)+1

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expand (sin((3t)/2)+cos((3t)/2))^2

expand

(sin (\frac{3 t}{2}) + cos (\frac{3 t}{2}))^{2}

sin (2 \cdot \frac{3 t}{2}) + 1

Solution steps

(sin (\frac{3 t}{2}) + cos (\frac{3 t}{2}))^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(sin (\frac{3 t}{2}) + cos (\frac{3 t}{2}))^{2} = sin^{2} (\frac{3 t}{2}) + 2 sin (\frac{3 t}{2}) cos (\frac{3 t}{2}) + cos^{2} (\frac{3 t}{2})

= sin^{2} (\frac{3 t}{2}) + 2 sin (\frac{3 t}{2}) cos (\frac{3 t}{2}) + cos^{2} (\frac{3 t}{2})

Simplify

sin^{2} (\frac{3 t}{2}) + 2 sin (\frac{3 t}{2}) cos (\frac{3 t}{2}) + cos^{2} (\frac{3 t}{2}) : sin (2 \cdot \frac{3 t}{2}) + 1

= sin (2 \cdot \frac{3 t}{2}) + 1

- ln (sin (x)) cos (x) + (- x - cot (x)) sin (x)

\frac{27 ( 4 - s ) ^{9}}{( - 4 s ^{3} + 48 s ^{2} - 192 s + 229 ) ^{3}}

(4 + i x)^{2}

- 2 (1 + 2)

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

What is expand (sin((3t)/2)+cos((3t)/2))^2 ?
The solution to expand (sin((3t)/2)+cos((3t)/2))^2 is sin(2*(3t)/2)+1