Sqrrtcos2x ​ + (1+sin2x) ​ =2 (sinx+cosx) ​ , if-

int(sin2x)/((sinx+cosx)^2)dx

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is

int _0^(pi/2) (sin^2x)/(sinx+cosx)dx

The value of int(sinx+cosx)/(sqrt(1-sin2x))\ dx is equal to (a) sqrt(sin2x)+C (b) sqrt(cos2x)+C (c) +-(sinx-cosx)+C (d) +-log(sinx-cosx)+C

If tanx=b/a , then sqrt((a+b)/(a-b))+sqrt((a-b)/(a+b)) is equal to (a) 2sinx//sqrt(sin2x) (b) 2cosx//sqrt(cos2x) (c) 2cosx//sqrt(sin2x) (d) 2sinx//sqrt(cos2x)

If y= (sinx+cosx)+(sin4x+cos4x)^(2) , then :

If f(x) = \begin{vmatrix} cos2x & cos2x & sin2x \\ -cosx & cosx & -sinx\\ sinx & sinx & cosx \end{vmatrix} then

The derivative of tan^(-1) ((sinx -cosx)/(sinx +cosx)) , with respect to (x)/(2) , where x in(0,(pi)/(2)) is:

The value of |(cos(x-a), cos(x+a), cosx),(sin(x+a), sin(x-a), sinx),(cosatanx, cosacotx, cosec2x)|= (A) 1 (B) sina cosa (C) 0 (D) sinx cosx

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 solution set of sinx + cosx -2sqrt(2) sin x cosx=0 is completely described by