Using cos 15 degrees sq rt of 6 sq rt of 2 4 find the EXA

Using cos 15 degrees = (sq rt of 6 + sq rt of 2) / (4), find the EXACT value for cos 7.5 degrees. To get a completely simplified answer, you will have to combine fractions and also rationalize a denominator--twice. Your answer should consist of one fraction with radicals in only the numerator.

Solution

given cos15^o = (6+2)/(4)

cos(a/2)=[(1+cosa)/2]

cos(7.5^o)=[(1+cos15^o)/2]

cos(7.5^o)=[(1+ (6+2)/(4))/2]

cos(7.5^o)=[(4+ 6+2)/(4*2)]

cos(7.5^o)=[(4+ 6+2)/8]

cos(7.5^o)=[(4+ 6+2)]/[8]

cos(7.5^o)=[(4+ 6+2)]/[22]

rationalise denominator multiply and divide by 2

cos(7.5^o)=[2*(4+ 6+2)]/[22 *2]

cos(7.5^o)=[(8+ 26+ 22)]/[4]