Question

sin 30° + cos 40° + tan 180° =​

Answer 1

• sin² 120° + cos² 150° + tan²120° + cos 180° - tan 135° =4.5
• Step-by-step explanation:

We know trigonometry relation

sin(120°) = sin(180° -60°) = sin 60°

cos (150°) =cos(180°-30°) = -cos 30°

tan(120°) =tan (180°-60°) = -tan 60°

tan (135°) =tan(180°-135°)= -tan 45°

We know value of trigonometry ratio for angle

$\mathbf{\sin 60^{\circ}=\frac{\sqrt{3}}{2}}$

$\mathbf{\cos 30^{\circ}=\frac{\sqrt{3}}{2}}$

$\mathbf{\tan 60^{\circ}=\sqrt{3}}$

• tan 45° =1
• cos 180° = -1

Now come to question

• sin² 120° + cos² 150° + tan²120° + cos 180° - tan 135°

• sin² 60° + cos² 30° + tan²60° + cos 180° + tan 45°

On putting respective value in above equation

$\mathbf{\frac{3}{4}+\frac{3}{4}+3-1+1}$

$\mathbf{\frac{6}{4}+3}$

This is answer