" 13.Let "(3 pi)/(4)

Let (3 pi)/(4)

f(x)=min(sin x,cos x),x in(-pi,pi) the values of x where f(x) is non differentiable,is the set A. Then A is subset of (A) {(-3 pi)/(4),(-pi)/(4),(3 pi)/(4)}(B){(-pi)/(4),(pi)/(4),(3 pi)/(3)}(C){(-3 pi)/(4),(3 pi)/(4)}(D){(-3 pi)/(4),(pi)/(4),(pi)/(4),(3 pi)/(4)}

The possible values of theta in (0, pi) such that sin (theta) + sin (4 theta) + sin (7 theta) = 0 are (1) (2 pi) / (9), (i) / (4 ), (4 pi) / (9), (pi) / (2), (3 pi) / (4), (8 pi) / (9) (2) (pi) / (4), (5 pi ) / (12), (pi) / (2), (2 pi) / (3), (3 pi) / (4), (8 pi) / (9) (3) (2 pi) / (9 pi) ), (pi) / (4), (pi) / (2), (2 pi) / (3), (3 pi) / (4), (35 pi) / (36) (4) (2 pi ) / (9), (pi) / (4), (pi) / (2), (2 pi) / (3), (3 pi) / (4), (8 pi) / (9)

Prove that (i) " tan"^(2) .(pi)/(3) + 2cos^(2) .(pi)/(4)+ 3 sec^(2).(pi)/(6)+ 4 cos^(2).(pi)/(2)=8 (ii) " sin ".(pi)/(6) " cos 0 + sin ".(pi)/(4) " cos " .(pi)(4) + " sin " .(pi)/(3) "cos " .(pi)/(6) =(7)/(4) (iii) " 4sin " (pi)/(6) " sin"^(2) (pi)/(3) + 3 " cos " .(pi)/(3) " tan ".(pi)/(4) = " cosec"^(2).(pi)/(2)=4

The range of f(x)=cot^(-1)(log_(1/2)(x^(4)-2x^(2)+3)) is ( (pi)/(2) (3 pi)/(4) 0 (3 pi)/(4) pi) (0 (3 pi)/(4)

Let lambda=tan((3 pi)/(4)-(1)/(4)sin^(-1)(-(4)/(5)))then(lambda^(2)-lambda+22)^(2)is

Let I=int_((pi)/(4))^((pi)/(3))(sinx)/(x)dx . Then

Let P=(("cos"(pi)/(4),-"sin"(pi)/(4)),("sin"(pi)/(4),"cos"(pi)/(4))) and X=(((1)/(sqrt(2))),((1)/(sqrt(2)))) . Then P^(3)X is equal to

Let Q = [{: (cos ""(pi)/(4) , - sin""(pi)/(4)),(sin""(pi)/(4), cos""(pi)/(4)):}] and x = [{:((2)/(sqrt(2))),((1)/(sqrt(2))):}] then Q^(3) x is equal to