" (1) "cos^(-1)((sin t cos^(2)x)/(sqrt(2)))^((5 pi)/(4)ln cot)(9 pi)/(4)

cos^(-1)((sin x+cos x)/(sqrt(2))),(pi)/(4) lt x lt (5pi)/4

The value of sin^(-1)(cot(sin^(-1)((2-sqrt(3))/(4)+(cos^(-1)(sqrt(12)))/(4)+sec^(-1)sqrt(2))))(a)0( b) (pi)/(2)( c) (pi)/(3)( d) none of these

Prove that cos^-1 ((sin x + cos x )/(sqrt2)) = x - (pi/4), (pi/4) le x le ((5pi)/4)

prove that tan^(-1)((cos x)/(1-sin x))-cot^(-1)((sqrt(1+cos x))/(sqrt(1-cos x)))=(pi)/(4),x varepsilon(0,(pi)/(2))

Evalute : "sin"^(2)(pi)/(4) + "cos"^(2) (3pi)/(4)+"cos"^(2)(5pi)/(4)+"sin"^(2)(7pi)/(4).

Let g(x)=sqrt(sin^(-1)(cos(tan^(-1)x))+cos^(-1)(sin(cot^(-1)x))) ,then int_(-sqrt((pi)/(2)))^(sqrt((pi)/(2)))g(x)dx equals

cos ((5pi)/(4)) - sin ((5pi)/(4)) + tan((11pi)/(4)) - cot((11pi)/(4))=

int_(0)^((pi)/(2))(cos^(2)x)/(sin x+cos x)dx=(1)/(sqrt(2))(log(sqrt(2)+1))

Prove that (i) "cos " ((pi)/(3) +x) =(1)/(2) ( " cos " x - sqrt(3) sin x) (ii) " sin " ((pi)/(4) + x) + " sin " ((pi)/(4)-x) =sqrt(2) " cos " x (iii) (1)/(sqrt(2)) " cos ((pi)/(4) + x) = (1)/(2) " (cos x - sin x) " (iv) " cos x + cos " ((2pi)/(3) +x) + " cos " ((2pi)/(3)-x) =0

(sec^(2)(pi)/(4)-cot^(2)(pi)/(4))/(sin^(2)(pi)/(3)+cos^(2)(pi)/(6))+(sin^(2)(pi)/(2)-cos^(2)(pi)/(3))/((1)/(4)tan^(2)(pi)/(6))=9(2)/(3)