Question

If a sin^3x + b cos^3x = sin x cos x and
a sin x = b cos x then a² + b^2=

Answer 1

Answer:

see below

Step-by-step explanation:

asin

3

x+bcos

3

x=sinx cosx

Substituting asinx=bcosx, we get

asin

3

x+b cos

3

x=sinx cosx

b cosx sin

2

x+bcos

3

x=sinx cosx

bcosx (sin

2

x+cos

2

x)=sinx cosx

Solving this we get

b=sinx and a=cosx

Hence,

a

2

+b

2

=sin

2

x+cos

2

x=1