Question

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

Answer 1

Answer:

4.5

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Step-by-step explanation:

Answer 2

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

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

        $\mathbf{\frac{6}{4}+3}$ =4.5  = This is answer