Question

sin (180° + x). cos (270° - x) + cos (180° - x). sin (270° + x) = 1
​

Answer 1

Given:

sin (180° + x). cos (270° - x) + cos (180° - x). sin (270° + x) = 1

To find:

​To prove: sin (180° + x). cos (270° - x) + cos (180° - x). sin (270° + x) = 1

Solution:

From given, we have,

sin (180° + x). cos (270° - x) + cos (180° - x). sin (270° + x) = 1

Now consider L.H.S:

sin (180° + x). cos (270° - x) + cos (180° - x). sin (270° + x)

we use the properties:

sin (180° + x) = -sin x

cos (270° - x)  = -sin x

cos (180° - x) = -cos x

sin (270° + x) =  -cos x

so, we get,

= (-sin x) × (-sin x) + (-cos x) (-cos x)

= sin² x + cos² x

= 1

= R.H.S

Hence proved.