1.

Recall that sinx + cosx =u (say) and sin x cosx =v (say) are connected by (sinx +cosx)^(2) = sin^(2)x + cos^(2)x+2sin cosx rArr u^(2) = 1+2v rArr v=(u^(2)-1)/(2) It follows that any rational integral function of sinx + cosx, and sinx cosx i.e., R(sinx + cosx, sinx cosx), or in our notation R(u,v) can be transformed to R(u, (u^(2)-1)/2). Thus, to solve an equation of the form R(u,v)=0, we form a polynomial equation in u and than look for solutions. The number of solutions of the equation sin theta + costheta=1 + sintheta costheta in the interval [0,4pi] is

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FOUR
Six
Eight
FIVE

ANSWER :A


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