Question

If tan theta + cot theta =2 . Find the values of (1) Tan square theta+cot square theta. (2) Tan cube theta + cot cube theta. (3) Tan raise to power 4 theta +cot raise to power 4 theta

Answer 1

simple one.. whole the given term ..and you will get tan square theta + cot square theta + 2tan theta multiply cit theta equal to 4..
in this expression tan theta multiply cot theta will be 1 .. so answer of 1st will be 2 and similarly you can solve the second one ..

Answer 2

tan theta+ cot theta = 2. ...(1)
on sq. both sides
tan sq.theta +cot sq. theta + 2tan theta×cot theta = 2×2
tan sq. theta + cot sq. theta+2 = 4
tan sq. theta + cot sq. theta= 2

and on cubing both sides
tan cube theta + cot cube theta +3tan theta ×cot theta (tan theta + cot theta) =8
tan cube theta + cot cube theta +3×2 = 8
tan cube theta + cot cube theta =8-6
tan cube theta + cot cube theta = 2