If theta in an acute angle and tan theta+cot theta=2.then find the value of tan^5theta+cot^5theta =?
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Answered by
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Given, tan theta + cot theta = 2
= tan theta + 1/tan theta = 2
= tan^2 theta + 1/tan theta = 2
= tan^2 theta + 1 = 2 tan theta
= tan^2 theta + 1 - 2 tan theta = 0
= (tan theta - 1)^2 = 0
= tan theta - 1 = 0
= tan theta = 1
theta = 45 degrees
So, tan^5 theta + cot^5 theta = (tan 45)^5 + (cot 45)^5
= 1^5 + 1^5
= 2
Hope this helps!
= tan theta + 1/tan theta = 2
= tan^2 theta + 1/tan theta = 2
= tan^2 theta + 1 = 2 tan theta
= tan^2 theta + 1 - 2 tan theta = 0
= (tan theta - 1)^2 = 0
= tan theta - 1 = 0
= tan theta = 1
theta = 45 degrees
So, tan^5 theta + cot^5 theta = (tan 45)^5 + (cot 45)^5
= 1^5 + 1^5
= 2
Hope this helps!
Sahupavan:
sorry Bhaiya i thank u r wrong
that is wrong answer
Thats okk..what is the correct answer?
sorry ans is correct but solution is wrong
ya fer u are not show full step
which is important
Hahaha...Tell me where u have doubt?
I have just simplified the steps. Shall i correct my answer. If u want me to correct then i can correct it. No worries.
Answered by
97
I hope that is right so follow
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me @SAHUPAVAN
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