Question

sin²60 + 2tan45 - cos²30​

Answer 1

Answer:

in2(60)+2tan45−cos2(30)=2

Step-by-step explanation:

To find : Evaluate \sin^260+2\tan 45-\cos^2 30sin260+2tan45−cos230

Solution :

Expression

\sin^2(60)+2\tan 45-\cos^2 (30)sin2(60)+2tan45−cos2(30)

Using trigonometry values,

\sin 60=\frac{\sqrt3}{2}sin60=23

\tan 45=1tan45=1

\cos 30=\frac{\sqrt3}{2}cos30=23

Substitute the values in the expression,

\sin^2(60)+2\tan 45-\cos^2 (30)=(\frac{\sqrt3}{2})^2+2(1)-(\frac{\sqrt3}{2})^2sin2(60)+2tan45−cos2(30)=(23)2+2(1)−(23)2

\sin^2(60)+2\tan 45-\cos^2 (30)=\frac{3}{4}+2-\frac{3}{4}sin2(60)+2tan45−cos2(30)=43+2−43

\sin^2(60)+2\tan 45-\cos^2 (30)=0+2sin2(60)+2tan45−cos2(30)=0+2

\sin^2(60)+2\tan 45-\cos^2 (30)=2sin2(60)+2tan45−cos2(30)=2

Therefore, \sin^2(60)+2\tan 45-\cos^2 (30)=2sin2(60)+2tan45−cos2(30)=2

Answer 2

I hope it is helpful for you.