Question

tanΦ+cotΦ=2...find tan^1000Φ+cot^100Φ

answer in details ​

Answer 1

Answer:

put Angle as 45

tan 45+ cot 45= 1

Ans will be 2

for the question

Answer 2

Answer:

tantheta+cottheta =2,

tantheta + (1/tantheta) =2;

tan squared theta +1 = 2tantheta;

tansquaredtheta -2tantheta +1 =0;

(tantheta -1)square =0;

So, tan theta = 1

theta = pi/4 + pi*n, n belongs to natural numbers.

Now, dealing with

tan squared theta - cot squared theta =

(tantheta+cottheta)(tantheta-cottheta)=

2*(tantheta - 1/tantheta) =

2*(tan squared theta -1)/tantheta =

-2*(1-tansquaredtheta)/tantheta=

-2*2*tantheta/(tantheta*tan2theta)=

-4/tan2theta =

-4/tan(2*pi/4 + 2*n*pi) =

-4/tan(pi/2 + 2*n*pi) = -4/(infinity) = 0

Or simply, tan theta =1, as found earlier.

So, tan squared theta - cot squared theta =

(tan theta) square - 1/(tan theta) square =

(1)square - (1)square = 1–1= 0.