Question

sin theta + 2cos theta =2 then (cos theta -2sin theta) is​

Answer 1

Answer:

If cos theta + sec theta = 2 what is the value of cos^100 theta +sec^100 theta?

Cos theta+sec theta =2

=> cos ^2 theta +1 = 2 cos theta

=> cos^2 theta -2 cos theta +1=0

Solving the above quadratic equation in cos theta,we get

cos theta =1

=>theta =cos inverse (1)

=>theta=2 n pi

Now we need to find the value of

cos 100 theta+sec 100 theta

Substitute the value of theta as theta=2 n pi:

=>cos 100 theta + sec 100 theta = cos 100 (2 n pi) + sec 100 (2 n pi)

=cos 2 (100n pi) + sec 2 (100n pi)

Let 100n=k , some variable

=>cos 100 theta + sec 100 theta = cos (2 k pi) + sec (2 k pi) = 1 + 1 = 2