Question #2712b

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Answer 1 · 2017-03-31T08:25:03

$1/sqrt 2$

$cos x = cos(x/2 + x/2) = cos^2 (x/2) -sin^2 (x/2) =2 cos^2 (x/2) -1$

$cos x = 2 cos^2 (x/2) -1$

$cos x + 1 = 2 cos^2 (x/2)$

$(1 + cos x)/2 = cos^2 (x/2)$

$+- sqrt((1 + cos x)/2) = cos (x/2)->$ proved for all $x$ .

To find their value when $x =pi/2$

A . $cos (x/2) = cos (pi/4) = 1/sqrt 2$

B. $+- sqrt((1 + cos x)/2) = +- sqrt((1 + cos (pi/2))/2)$

$= +- sqrt((1 + 0)/2) = +- sqrt(1/2) = +- sqrt1/sqrt 2 = +- 1/sqrt 2$
since $x$ in quadrant I, $sqrt((1 + cos x)/2) = 1/sqrt 2$