Home
Class 12
MATHS
Using mathematical induction, show that ...

Using mathematical induction, show that
`A^(n)=[(cos n theta,sin n theta),(-sin n theta,cos n theta)]` if `A=[(cos theta,sin theta),(-sin theta,cos theta)], n in N`

Text Solution

Verified by Experts

Consider `A^2=[[costheta,sintheta],[-sintheta,costheta]].[[costheta,sintheta],[-sintheta,costheta]]`
`A ^ 2 =[ [ cos ^ 2 θ −sin ^ 2 ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    NCERT ENGLISH|Exercise EXERCISE 12.2|11 Videos
  • PROBABILITY

    NCERT ENGLISH|Exercise EXERCISE 13.2|18 Videos

Similar Questions

Explore conceptually related problems

if A=[{:(costheta,sin theta ),(-sin theta,costheta):}] , then show that : A^(2)=[{:(cos2theta,sin2theta),(-sin2theta,cos2theta):}]

Prove the orthogonal matrices of order two are of the form [(cos theta,-sin theta),(sin theta,cos theta)] or [(cos theta,sin theta),(sin theta,-cos theta)]

(4) A=[[cos(theta),sin(theta)],[-sin(theta),cos(theta)]] ; prove, A^n=[[cos(ntheta),sin(ntheta)],[sin(ntheta),cos(ntheta)]]

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

Solve (3 sin theta-sin 3 theta)/(sin theta)+(cos 3 theta)/(cos theta)=1 .

(2 sin theta*cos theta - cos theta)/(1-sin theta+sin^2 theta-cos^2 theta) = cot theta

1 + (cos 2 theta + cos 6 theta)/(cos 4 theta) = (sin 3 theta)/(sin theta).

Show that the matrix [{:( cos theta , sin theta ),(-sin theta , cos theta ):}] is orthogonal

Show that costheta [[costheta, sintheta],[-sintheta, cos theta]] + sin theta [[sintheta ,-cos theta],[costheta, sin theta]] =1

Prove that (cos^3theta+sin^3 theta)/(cos theta+sin theta)+(cos^3 theta-sin^3 theta)/(cos theta-sin theta)=2