Question #6f9af

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Answer 1 · 2017-01-29T15:18:42

1)
$cos75^@$
$=cos(45+30)$

$=cos45cos30-sin45sin30$

$=1/sqrt2xxsqrt3/2-1/sqrt2xx1/2$
$=(sqrt3-1)/(2sqrt2)$

2)
$sin75^@$
$=sin(45+30)$

$=sin45cos30+cos45sin30$

$=1/sqrt2xxsqrt3/2+1/sqrt2xx1/2$
$=(sqrt3+1)/(2sqrt2)$

3)
$sin((17pi)/6)cos((8pi)/3)-cos((17pi)/6)sin((8pi)/3)$

$=sin((17pi)/6-(8pi)/3)$

$=sin((17pi)/6-(16pi)/6)$

$=sin(pi/6)=1/2$

4)

$cos((7pi)/5))cos((3pi)/5)-sin((7pi)/5))sin((3pi)/5)$

$=cos((7pi+3pi)/5)$

$=cos(2pi)=cos0=1$

5)

$(tan56-tan26)/(1+tan56tan26)$
$=tan(56-26)=tan30=1/sqrt3$

6)

$(tanpi/12+tanpi/6)/(1-tanpi/12tanpi/6)$

$=tan(pi/12+pi/6)$

$=tan((pi+2pi)/12)$

$=tan(pi/4)=1$