Find sin 5 pi6 16 13 12 Squareroot 22 Squareroot 32 Squarer

Find sin (5 pi/6). 1/6; 1/3; 1/2; Squareroot 2/2; Squareroot 3/2; - Squareroot 2/2; 0 -1/2 Find cos^-1 (sin (5 pi/6)). pi/6; -pi/6; pi/4; pi/3; -pi/3; 0 Find sin^-1 (sin (5 pi/6)). pi/6 -pi/6 pi/4 -pi/4 pi/3 -pi/3 5 pi/6 Simplify 1 + csc(theta)/cot(theta) + cos(theta). cot(theta) tan(theta) sec(theta) csc(theta) sin(theta) Find all solutions of cos(theta) = -1/2 in the interval [0 degree, 360 degree). 60 degree, -60 degree; 60 degree, 300 degree; 120 degree, 240 degree 210 degree, 330 degree; 30 degree, 150 degree; 30 degree, 330 degree Find the exact value of sin (pi/4 + pi/3). Squareroot 2 + Squareroot 6/4; Squareroot 2 - Squareroot 6/4; Squareroot 6 + Squareroot 2/4; -Squareroot 2 - Squareroot 6/4; Squareroot 2 + Squareroot 6/2 Find the exact value of cos(165 degree). Squareroot 2 + Squareroot 6/4; Squareroot 2 - Squareroot 6/4; Squareroot 6 + Squareroot 2/4; -Squareroot 2 - Squareroot 6/4; Squareroot 2 + Squareroot 6/2 Find the exact value of cos(2u) if sin(u) = 4/5 and 0

Solution

Question number 1,2 and 3 are absolutely correct.

4. (1 + csc theta)/(cot theta+cos theta)

csc theta= 1/sin theta , cot theta=cos theta/sin theta

(1 + 1/sin theta)/(cos theta/sin theta   + cos theta)= sin theta(sin theta +1)/ sin theta cos theta(1+sin theta)

                                                                                     = 1/cos theta=sec theta

Correct option is c

5. cos theta=-1/2

taking cos^-1 on both sides

theta=cos^-1(-1/2)=120,240 degree

Correct option is C

6. sin(pi/4 + pi/3)

This is of the form sin(A+B) = sinA cos B + cos A sin B

                              sin(pi/4 + pi/3) =sinpi/4 cos pi/3 + cos pi/4 sin pi/3 = (sqrt2)/4 + sqrt6/4= (sqrt2 + sqrt6)/4

Correct option is A