Question

the value of sin^230°- cos^230° is​

Answer 1

Answer:

-1/2

Step-by-step explanation:

sin^230°- cos^230°=(sin30°+ cos30°)(sin30°- cos30°)

                                                ∵ a²-b²=(a+b)(a-b)

Now, sin30°=1/2 and cos30°=√3/2

∴(sin30°+ cos30°)(sin30°- cos30°)=(1/2+√3/2)(1/2-√3/2)

=[(1+√3)/2][(1-√3)/2]

=(1+√3)(1-√3)/4

=(1-3)/4 ..... ∵ (a+b)(a-b)=a²-b²

=-2/4

= -1/2

SHORTCUT METHOD

sin30°=1/2 and cos30°=√3/2

∴ sin^230°=1/4 and cos^230°=3/4

∴ sin^230°- cos^230°=(1/4-3/4)=(1-3)/4

=-2/4

= -1/2

Answer 2

Answer:

See the above attachment

I hope it's helps u

Thank you