What is expand (1+cos(t))cos(t/2)+sin(t)sin(t/2) ?

The solution to expand (1+cos(t))cos(t/2)+sin(t)sin(t/2) is cos(t/2)+cos(t/2-t)

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expand (1+cos(t))cos(t/2)+sin(t)sin(t/2)

expand

(1 + cos (t)) cos (\frac{t}{2}) + sin (t) sin (\frac{t}{2})

cos (\frac{t}{2}) + cos (\frac{t}{2} - t)

Solution steps

(1 + cos (t)) cos (\frac{t}{2}) + sin (t) sin (\frac{t}{2})

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

Expand

cos (\frac{t}{2}) (1 + cos (t)) : cos (\frac{t}{2}) + cos (\frac{t}{2}) cos (t)

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

Use the Angle Difference identity:

cos (s) cos (t) + sin (s) sin (t) = cos (s - t)

= cos (\frac{t}{2}) + cos (\frac{t}{2} - t)

(5 sec (θ) + 2)^{2}

lo g_{10} (3) (x + 2)

\frac{( x - 1 ) ( x - 2 ) ( x - 3 )}{( 0 - 1 ) ( 0 - 2 ) ( 0 - 3 )}

e^{a} + e^{a} (x - a)

(1 + cos (α)) (1 + csc (α))

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