Find the value of cos11π/12?
2 Answers
Explanation:
"using the "color(blue)"trigonometric identity"
•color(white)(x)cos(x+y)=cosxcosy-sinxsiny
"note that "(11pi)/12=(2pi)/3+pi/4
cos((11pi)/12)=cos((2pi)/3+pi/4)
=cos((2pi)/3)cos(pi/4)-sin((2pi)/3)sin(pi/4)
=-cos(pi/3)cos(pi/4)-sin(pi/3)sin(pi/4)
=(-1/2xxsqrt2/2)-(sqrt3/2xxsqrt2/2)
=-sqrt2/4-sqrt6/4=-1/4(sqrt2+sqrt6)
Explanation:
Find
In this case:
Finally,
Check by calculator.
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