Question

find cos(40-theta) - sin (50 + theta) + 2( cos ^2 45 + tan ^2 60) - 6 ( sin ^2 45 - tan ^2 30)​

Answer 1

Answer:

Cos(40 - θ) - sin(50 + θ) + {cos²40° + cos²50°}/{sin²40° + sin²50°}

we know , sin(90° - x) = cosx and cos(90° - x) = sinx.

so, sin(50+ θ) = sin{90° -(40° - θ)} = cos(40° -θ)----(1)

cos40° = cos(90° - 50°) = sin50° ----(2)

from equations (1) and (2),

= cos(40° - θ) - cos(40° - θ) + (sin²50° + cos²50°)/(sin²40° + cos²40°)

[ sin²50° + cos²50° = 1 and sin²40° + cos²40° = 1]

= 0 + 1/1 = 1 [ans]

Answer 2

Step-by-step explanation:

hope it helps...............