sin 30° - sin 60° - cos 30° + cos 60° + tan 45° + tan 60° + cot 45° =?

Value of
sin 30° = 1/2
sin 60° = √3/2
cos 30° = √3/2
cos 60° = 1/2
tan 60° = √3
tan 45° = 1
cot 45° = 1


sin 30° - sin 60° - cos 30° + cos 60° + tan 45° + tan 60° + cot 45° =

Re-Arrange
( sin 30° + cos 60° ) + ( - sin 60° - cos 30° ) + tan 60° + tan 45 ° + cot 45° =

= (1/2 + 1/2) + (-√3/2 - √3/2) + √3 + 1 + 1
= 1 - √3 + √3 + 1 + 1
= 3

Answer = 3

hey listen tan45=cot45= 1..... now sin30=cos60= 1/2. .... tan60= root(3)..... and cos30= root(3)/2.... there we get the answer as tan45+cot45+ tan60+ sin30+cos60-sin60-cos30 as 1+1+root(3)+ 1/2 + 1/2 - root(3)/2- root(3)/2 which is 2+ root(3)+1- root(3). which is 3.

3

sin 30° - sin 60° - cos 30° + cos 60° + tan 45° + tan 60° + cot 45°
= 3

1/2 - sqrt(3)/2 - sqrt(3)/2 + 1/2 + 1 + sqrt(3) + 1
= 3

1/2 - √3/2 - √3/2 + 1/2 + 1 + √3 + 1 = 3

3

3

sin 30° - sin 60° - cos 30° + cos 60° + tan 45° + tan 60° + cot 45° =

= (1/2) - (√3/2) - (√3/2) + (1/2) + 1 + √3 + 1

= [(1/2) + (1/2) + 1 + 1] + [-(√3/2) - (√3/2) + √3]

= 3

...
sin 30° - sin 60° - cos 30° + cos 60° + tan 45° + tan 60° + cot 45° =
0.50. . - 0.87 . . .- 0.87 . . + 0.50 . . .+ 1.0 . . . + 1.7 . . . + 1.0 = 2.46

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3

Sin 30° - sin 60° - cos 30° + cos 60° + tan 45° + tan 60° + cot 45°
= 1/2 - √3/2- √3/2 + 1/2 + 1 + √3 +1
= 3

sin30=cos60, sin60=cos30, tan45=cot45=1
1/2-√3/2-√3/2+1/2+1+√3+1=3-√3+√3=3

Notation: Put s = sin, c = cos, t = tan, ct = cot. Then s30 - s60 - c30 + c60 + t45 + t60 +ct45
= (1/2) - (1/2)rt3 - (1/2)rt3 + (1/2) + 1 +rt3 + 1 = 3

3

3