Question

if cos theta + sec theta=2 find cos raise to 5 +sin raise to 5

Answer 1

Answer:

I don't know...... ......

Answer 2

Step-by-step explanation:

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

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cosx+1cosx=2

cos2x+1=2cosx

cos2x−2cosx+1=0

(cosx−1)2=0

cosx=1

secx=1

(cosx)^100 + (secx)^100 = 2

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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