To `cos(A+B)=cosx.cosy - sin x sin "and hence find "cos75^(@)`

Prove geometrically that cos(x + y) = cos x cos y - sinx sin y and hence prove cos((pi)/(2) + x) = - sin x .

Prove Geometrically cos(x+y)=cosx,cosy-sinx.siny and hence prove that cos(x-y)= cosxcosy+sinxsiny using unit circle concept ?

If sin(A+B)=sinAcosB+cosAsinB and cos(A-B)=cosAcosB+sinAsinB , find the values of (i) sin75^(@) and (ii) cos15^(@) .

(a)Derive geometrically that cos(x+y)=cos x cos y-sin x sin y .Hence deduce the valueof cos 75^@

If sin (A-B)=sin A cos B-cos A sin B and cos (A - B) = cos A cos B + sin A sin B . find the values of sin 15^@ and cos 15^@.

If sin A=(1)/(sqrt(5)) and sin B=(1)/(sqrt(10)) ,find the values of cos A and cos B .Hence using the formula cos(A+B)=cos A cos B-sin A sin B, show that (A+B)=45^(@).

If 2cosx+2cos3x=cosy and 2sinx+2sin3x=siny then cos 2x=