Evaluate
cos (40°+0) - sin (50°-8) +
cos² 40° + cos² 50°/
sin² 40° + sin² 50°
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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]
Hope it helps you ✌️✌️❤️❤️
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