Find the value ? #sin105^@ + cos105^@#

2 Answers
Bill Jorgensen
May 20, 2018

#1/sqrt2#

Explanation:

#sin105^@ + cos105^@#

#sin(60^@+45^@) + cos(60^@+45^@) #

Sum identities:
#sin(alpha +beta) = sin(alpha)cos(beta) +cos(alpha)sin(beta)#
#cos(alpha +beta) = cos(alpha)cos(beta) -sin(alpha)sin(beta)#

#sin60^@ = sqrt3/2#

#sin45^@=sqrt2/2#

#cos60^@=1/2#

#cos45^@=sqrt2/2#

#(sqrt3/2*sqrt2/2+1/2*sqrt2/2) + (1/2*sqrt2/2 -sqrt3/2*sqrt2/2 ) = 1/sqrt2#

Nghi N
May 21, 2018

#sqrt2/2#

Explanation:

Use trig identity:
#sin x + cos x = sqrt2cos (x - 45)#
In this case:
#sin 105 + cos 105 = sqrt2cos (105 - 45) = sqrt2cos (60)#
Trig table gives #cos 60 = 1/2#, therefor:
#sin 105 + cos 105 = sqrt2/2#

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