If `z=1/(1-cos theta-i sin theta),` then `Re(z)` is a. `0` b. `1/2` c. `cot(theta/2)` d. `1/2 cot (theta/2)`

If z=1-costheta+isintheta,\ t h e n\ |z| is equal to a. 2sin(theta/2) b. 2cos(theta/2) c. 2\ |sin(theta/2)| d. 2\ |cos(theta/2)|

If a=costheta+isintheta, then (1+a)/(1-a) is: (a) . cot(theta/2) (b) . cottheta (c) . icot(theta/2) (d) . itan(theta/2)

If pi lt theta lt 2pi then sqrt ((1+cos theta)/(1-cos theta))= a. cosec theta+cot theta , b. cosec theta - cot theta , c. cot theta-cosec theta , d. -cosectheta - cot theta

Solve 2 tan theta-cot theta=-1 .

Prove that ( cos theta + cos 2 theta + cos 3 theta + cos 4 theta)/(sin theta + sin 2 theta + sin 3 theta + sin 4 theta)= cot ""(5theta)/(2).

The value of cos^2(pi/6+theta)-sin^2\ \ (pi/6-theta) is a, 1/2cos2theta b. 0 c. -1/2cos2theta d. -cot35^0

(1+tan theta+sec theta)(1+cot theta-cosec theta) = ? (a) -1 (b) 0 (c) 2

If pi < theta < 2pi and z=1+cos theta + i sin theta , then write the value of |z|

From algebra we know that if ax^(2) +bx + c=0 , a( ne 0), b, c int R has roots alpha and beta then alpha + beta=-b/a and alpha beta = c/a . Trignometric functions sin theta and cos theta, tan theta and sec theta, " cosec " theta and cot theta obey sin^(2)theta + cos^(2)theta =1 . A linear relation in sin theta and cos theta, sec theta and tan theta or " cosec "theta and cos theta can be transformed into a quadratic equation in, say, sin theta, tan theta or cot theta respectively. And then one can apply sum and product of roots to find the desired result. Let a cos theta, b sintheta=c have two roots theta_(1) and theta_(2) . theta_(1) ne theta_(2) . The vlaue of cos(theta_(1) + theta_(2)) is a and b not being simultaneously zero)

If cosec theta + cot theta = p prove that cos theta = p2-1 / p2 + 1