Question

(sin 24 degree cos 6 degree) -(sin6 degree sin 66 degree)/(sin21 degree cos 39 degree) -(cos51 degree sin 69 degree)

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

x = -1

Step-by-step explanation:

We know that,

(1)sin(90∘−x)=sin(π2−x)=cosx

(2)cos(90∘−x)=cos(π2−x)=sinx

(3)sinAcosB−cosAsinB=sin(A−B)

We take,

X=sin24°cos6°−sin6°sin66°sin21°cos39°−cos51°sin69°

using:(1)and(2)

sin66∘=sin(90∘−24∘)=cos24∘

cos51∘=cos(90∘−39∘)=sin39∘

sin69∘=sin(90∘−21∘)=cos21∘

So,

X=sin24°cos6°−sin6°cos24°sin21°cos39°−sin39°cos21°

X=sin(24∘−6∘)sin(21∘−39∘)...→[Apply(3)]

X=sin18∘sin(−18)

X=(sin18∘−sin18∘)...→[∵sin(−θ)=−sinθ]

X=−1