`cos mtheta + cos ntheta=0`

cosm theta - sin ntheta =0

Solve the following trigonometric equations,(i) sin mtheta+"sin" theta=0 (ii) cos m theta-cos ntheta=0 (iii) "sin" 2theta+costheta=0 (iv) "sin"3theta+cos2theta=0

The value of (sintheta+i cos theta)^n is (A) sin n theta+i cos ntheta (B) cos ntheta-i sin n theta (C) cos ((npi)/2- ntheta)+is sin ((npi)/2- ntheta) (D) none of these

The value of (sintheta+i cos theta)^n is (A) sin n theta+i cos ntheta (B) cos ntheta-i sin n theta (C) cos ((npi)/2- ntheta)+is sin ((npi)/2- ntheta) (D) none of these

If ((1 + cos theta + i sin theta ) /(i+ sin theta + i cos theta ))= cos ntheta + i sin n theta then n is equal to :

Evaluate the following limits.(ii) underset (theta rarr 0) ((1-cos mtheta)/(1-cos n theta))

If [frac{1+costheta+isintheta}{i+sintheta+icostheta}]^4 = cos ntheta+isin ntheta , then n is equal to

Using mathematical induction prove that, costheta+cos2theta+ . . .+cosntheta=("cos"(n+1)/(2)theta"sin"(ntheta)/(2))/("sin"(theta)/(2)) .

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