Question

Evaluate 2 sin 60° + tan 45° + cos²60°​

Answer 1

1.25+√3 or 2.9821 to the nearest ten thousandth.

Explanation:

sin 60 = √3/2, tan 45 = 1 and cos^2 60 = (1/2)^2 = 1/4

So we get 2 *√3/2 + 1 + 1/4

= √3 + 1.25

Answer 2

`\boxed{\sf 2sin \: 60 ^( \circ) + tan \: 45^( \circ) + {cos}^(2) \ 60^(\circ) = 2.98}`

Explanation:

We know:

`\sf sin \: 60 ^( \circ) = ( √(3) )/(2) \\ \\ \sf tan \: 45 ^( \circ) = 1 \\ \\ \sf cos \: 60 ^( \circ) = (1)/(2)`

So,

`\sf \implies 2sin \: 60 ^( \circ) + tan \: 45^( \circ) + {cos}^(2) \: 60^( \circ) \\ \\ \sf \implies \cancel{2} * \frac{ √(3) }{ \cancel{2}} + 1 + {( (1)/(2)) }^(2) \\ \\ \sf \implies √(3) + 1 + {( (1)/(2)) }^(2) \\ \\ \sf \implies √(3) + 1 + (1)/(4) \\ \\ \sf \implies √(3) + 1 + 0.25 \\ \\ \sf \implies 1.25 + √(3) \\ \\ \sf \implies 1.25 + 1.73 \\ \\ \sf \implies 2.98`