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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