sin 2 120 ∘ +cos 2 150 ∘ +tan 2 120 ∘ +cos180 ∘ −tan135 ∘
Answers
Answer:
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}}sin60
∘
=
2
3
\mathbf{\cos 30^{\circ}=\frac{\sqrt{3}}{2}}cos30
∘
=
2
3
\mathbf{\tan 60^{\circ}=\sqrt{3}}tan60
∘
=
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}
4
3
+
4
3
+3−1+1
\mathbf{\frac{6}{4}+3}
4
6
+3 =4.5 = This is answer
Answer:
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