Question

The value of cos²60⁰ + sin²60⁰ - tan²45⁰ = _______​

Answer 1

4( sin +30° + cos²60°) - 3( cos²45° - sin²90°) - sin²60°

=> 4 [(1/2) + (1+ 2)²} - 3 { ( 1 / √2 )²-(1)²} - (√3/2)²

=> 4 [1/16 + 1/4)-3(1/2-1)-(3/4)

=> 4 ((1+4) / 16 ]-3 {(2-1)/2}-(3/4)

=> 4 x 5/16 - 3x1/2-3/4

=> 5/4-3/2-3/4

=> (5-6-3)/4

=> - 4/4

=> -1

..The required Answer is - 1

Since,

sin30° = 1/2

cos60° = 1/2

cos45° = 1/ √2

sin90° = 1

sin60° = √3/2