Question

Show that 2(sin 60° + cos 30") - 3(tan-60° - tan-45°) + 5cos 45º = 1​

Answer 1

Step-by-step explanation:

We know that ..

sin 60° = √3/2

cos 30° = √3/2

tan 60° = √3

tan 45° = 1

cos 45  = 1/√2

Substituting all the values,

LHS = 2(√3/2 + √3/2 ) - 3( √3 - 1 ) + 5(1/√2 )

      = 2√3 - 3√3 - 3 + 5/√2

      = -1/√3 - 3 + 5/√2

      ≈ -1 -3 + 5

      ≈ 5 - 4

      = 1 = RHS

     Hence proved..