Prove that : `(sin i)/(1+cos i)=(1-cos i)/(sin i)`

Prove that (i)(1-sqrt(3)i)=2((cos)(pi)/(3)-i(sin)(pi)/(3))

Express the following in a + ib form: (a) ((cos alpha + i sin alpha)^(4))/((sin beta + i cos beta)^(5)) (b) ((1+ cos phi + i sin phi)/(1 + cos phi - isin phi))^(n) (c) ((cos alpha + i sin alpha)(cos beta + i sin beta))/((cos gamma + i sin gamma)(cos delta + i sin delta))

Prove that : (1-cos theta+i sin theta)/(1+i sin theta+cos theta)=ie^(-1)tan((theta)/(2))

Prove that : (i) "sin"105^(@)+cos105^(@)=(1)/(sqrt(2)) (ii) cos105^(@)+cos15^(@)="sin"75^(@)-"sin"15^(@)

Prove that (i) (tan A+ sin A)/(tan A- sin A)= (sec A+1)/(sec A-1) (ii) (cot A- cos A)/(cot A+ cos A)= ("cosec" A-1)/("cosec" A+1)

In triangle ABC, right-angled at B. if tanA=1/(sqrt(3)) find the value of: (i) sin A cos C+cos A sin C(i i) cos A cos C sin A sin C

If A,B, C are the angles of a triangle ABC then (cos A+i sin A)(cos B+i sin B)(cos C+i sin C)

Prove each of the following identities : (i) (1+ cos theta + sin theta)/(1+ cos theta - sin theta) =(1+ sin theta)/(cos theta) (ii) (sin theta + 1- cos theta)/(cos theta - 1 + sin theta) = (1+ sin theta)/(cos theta)

Prove that : (i) sin42^(@)cos48^(@)+sin48^(@)cos42^(@)=1 (ii) cos70^(@)cos20^(@)-sin70^(@)sin20^(@)=0