`1/(cos theta-isin theta)`

Prove that (cos^3 theta-sin^3 theta)/(cos theta-sin theta) = 1+cos theta sin theta

Find the value of (1+cos theta+sin theta)/(1-cos theta +sin theta)

If ((4i^(3)-i)/(2i+1))^(2)=r(cos theta+isin theta) , then cos theta+sin theta is equal to (where, i^(2)=-1 )

Express the following in a + ib form: (i) ((cos theta+ isin theta)/(sin theta + icos theta))^(4) (ii) ((cos 2theta -isin2theta)^(4)(cos4theta +isin4theta)^(-5))/((cos 3theta +isin3theta)^(-2) (cos 3theta -isin 3theta)^(-9)) (iii) ((sinpi//8 +icos pi//8)^(8))/((sinpi//8-icospi//8)^(8))

Prove : (cos theta)/(1+sin theta) + (cos theta)/(1-sin theta)= 2 sec theta

Prove that (sec theta+tan theta -1)/(tan theta -sec theta +1)=cos theta/(1-sin theta)

y=1/((1+tan theta)^(sin theta-cos theta)+(cot theta)^(cos theta-cot theta))+ 1/((1+tan theta)^(cos theta-sin theta)+(cot theta)^(sin theta-cottheta)) +1/((1+tan theta)^(cos theta-cot theta)+(cot theta)^(cot theta-sin theta)) then (dy)/(dx) at theta=pi/3 is

Express the following in a+i b form: ((cos2theta-isin2theta)^4(cos4theta+isin4theta)^(-5))/((cos3theta+isin3theta)^(-2)(cos3theta-isin3theta)^(-9))

Prove, by induction, that (cos theta + isintheta)^n = cos n theta + isin ntheta for all positive as well as negative integral values of n

Prove that (1- cos theta + sin theta)/( 1+cos theta +sin theta) = "tan"(theta)/(2) .