Given that `sinx+siny=a and cosx+cosy=b` rajan derived the value of `tan((x+y)/2)` as follows. Fill in the blanks and write the complete solution. Given that `sinx+siny=a` and `cosx+cosy=b`.

Prove that (sinx-siny)/(cosx+cosy)=tan(x-y)/2

Prove that (sinx+sin3x)/(cosx+cos3x)=tan2x

Nikolas is asked to prove that cos^2 x+cos^4 x=1 if sinx+sin^2x=1 He proceeded as follows. But he could not complete the solution. Observe the solution and write the complete solution. Given that sinx+sin^2x=1 therefore sinx=1-sin^2x sinx=cos^2x ...............

If sinx +siny +sinz =0 = cos x +cosy +cosz , then find the value of expression cos(theta-x)+cos(theta-y)+cos(theta-z) .

Given that x^(2)+x-6 is a factor of 2x^(4)+x^(3)-ax^(2)+bx+a +b-1 , find the values of a and b.

prove the following (sin 5x+sinx-2sin3x)/(cos5x-cosx) = tanx

If (sinx)/(siny)=(1)/(2),(cosx)/(cosy)=(3)/(2) , where x,y in (0,(pi)/(2)) , then the value of tan (x+y) is equal to

Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals f(x)=sinx+cosx ,x in [0,pi]