If tanx+cotx=2 then find the value of tan^7x+cot^7x
Answers
Answered by
12
heya...!!!!
tanx + cotx = 2
=>tanx + 1/tanx = 2
=> tan²x + 1 = 2tanx
=> tan²x - 2tanx + 1 = 0
=> tan²x - tanx - tanx + 1 = 0
=> tanx(tanx - 1) - 1(tanx - 1) = 0
=> (tanx - 1)(tanx - 1)
=> tanx = 1,1
=> tanx = 1/cotx = 1
=> cotx = 1
now,
tan^7x + cot^7x
=> (1)^7 + (1)^7
=> 1 + 1
=> 2
tanx + cotx = 2
=>tanx + 1/tanx = 2
=> tan²x + 1 = 2tanx
=> tan²x - 2tanx + 1 = 0
=> tan²x - tanx - tanx + 1 = 0
=> tanx(tanx - 1) - 1(tanx - 1) = 0
=> (tanx - 1)(tanx - 1)
=> tanx = 1,1
=> tanx = 1/cotx = 1
=> cotx = 1
now,
tan^7x + cot^7x
=> (1)^7 + (1)^7
=> 1 + 1
=> 2
Answered by
3
Answer:
your answer attached in the photo
Attachments:
Similar questions