Home
Class 12
MATHS
If A={:[(cos theta,isintheta),(i sinthet...

If `A={:[(cos theta,isintheta),(i sintheta,costheta)]:},` then prove by principle of mathematical induction that `A^(n)={:[(cosntheta,isintheta),(isintheta,cosntheta)]:}` for all `n in N.`

Promotional Banner

Similar Questions

Explore conceptually related problems

For all ninNN , prove by principle of mathematical induction that, (costheta+isintheta)^(n)=cosntheta+isinntheta" "[i=sqrt(-1)] .

(costheta + isintheta)^4/(sintheta + icostheta)^5 is equal to.

For all ninNN , prove by principle of mathematical induction that, 2^(3n)-1 is divisible by 7.

If A={:[(3,-4),(1,-1)]:}, then by principle of mathematics induction show that, A^(n)={:[(1+2n,-4n),(n,1-2n)]:} for all n in N.

If A=[(costheta,sintheta),(-sintheta,costheta)] , then prove that A^(n)=[(cosntheta,sin n theta),(-sin ntheta,cos n theta)], n in N .

For all ninNN , prove by principle of mathematical induction that, 12^(n)+25^(n-1) is divisible by 13.

For all ninNN , prove by principle of mathematical induction that, 4^(n)+15n-1 is a multiple of 9.

For all ninNN , prove by principle of mathematical induction that, 15^(2n-1)+1 is divisible by 16.

If (1+2i)/(2+i)=r(costheta+isintheta) then

For all ninNN , prove by principle of mathematical induction that, 1+3+5+ . . .+(2n-1)=n^(2) .