Question

Let x and y be arbitrary angles.
a. Use the result of Exercise 1a (see answer for 1a below) to prove that sin x cos x >= (-1/2)
b. Use the facts that sin (-y) = -sin y and cos (-y) = cos y to prove that sin x cos x <= 1/2.
c. Prove that sin x + cos x <= sqrt (2)


1a) (sin x+ cos x)^2= (sin x)^2 + (cos x)^2 + 2 sin x cos x
since (sin x)^2 + (cos x)^2 =1
so the answer is 1 + 2 sin x cos x

Answer 1

aliter 1a:
sin2x >=-1
2 sinx cosx >= -1
sinx cosx >= -1/2

1c:
sin(x+45)<=1
expand sin(A+B)=sinA cosB + cosA sinB;
sinx cos45 + cosx sin 45 <=1
sinx+cosx<=sqrt2

Answer 2

wat is the answer for part b?

Answer 3

1b.
sin2x<=1
2 sinx cosx <=1
sinx cosx <= 1/2

Answer 4

and what do you mean by this "aliter 1a:"?

Answer 5

are you there sir/maam?