If #tan^4θ - tan^2θ = 1 #; then #cot^4θ + cot^2θ = ? #

1 Answer
Binayaka C.
Jun 19, 2017

#cot^4 theta+cot^2theta=1#

Explanation:

#tan^4 theta-tan^2theta=1 or tan^4 theta=tan^2theta+1 or tan^4 theta = sec^2theta or sin^4 theta/cos^4 theta=1/cos^2theta # or

#sin^4 theta/cos^2 theta=1 or cos^2theta/sin^4theta=1#

#cot^4 theta+cot^2theta=cot^2theta(1+cot^2theta)#

# = cot^2theta*csc^2theta= cos^2theta/sin^2theta*1/sin^2 theta#

#=cos^2theta/sin^4 theta= 1 #

#:. cot^4 theta+cot^2theta=1# [Ans]

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