`cos (40^(@)+theta)-sin (50^(@)-theta)=`

Show that: sin (40^(@) + theta) cos (10^(@) + theta) -cos(40^(@) + theta) sin (10^(@) + theta) = (1)/(2)

Without using trigonometric tables,evaluate each of the following: (sin^(2)20^(@)+sin^(2)70^(@))/(cos^(2)20^(0)+cos^(2)70^(@))+(sin(90^(@)-theta)sin theta)/(tan theta)+(cos(90^(@)-theta)cos theta)/(cot theta)+cos(40^(0)+theta)-sin(50^(@)-theta)+(cos^(2)40^(0)+cos^(2)50^(@))/(sin^(2)40^(0)+sin^(2)50^(@))

sin(50^(@)+theta)-cos(40^(@)-theta)

Solve cos(50^(@)+ theta) = sin (30^(@)+theta) .

sin (50^(@)+theta)-cos (40^(@) - theta)= _______

Prove that, sin(40^(@)+theta)cos(10^(@)+theta)-cos(40^(@)+theta)sin(10^(@)+theta)=(1)/(2)

Prove that : sin (40^@+theta)cos (10^@+theta)-cos (40^@+theta) sin (10^@+theta)=1/2 .

Prove that (i) sin(40^(@)-theta)-cos(50^(@)+theta)=0 (ii) sec(65^(@)+theta)-"cosec"(25^(@)-theta)=0

Prove that (i) sin(40^(@)-theta)cos(50^(@)+theta)=0 (ii) 1sec(65^(@)+theta)-"cesec"(25^(@)-theta)=0

Prove that (i) " sin " (50^(@) + theta ) " cos " (20^(@) + theta) - " cos " (50^(@) + theta) " sin " (20^(@) + theta) =(1)/(2) (ii) " cos " (70^(@) + theta ) " cos " (10^(@) + theta ) + " sin " (70^(@) + theta) " sin " (10^(@) + theta)=(1)/(2)