Get 2 FREE Instant-Explanations on Filo with code FILOAPP

If is an acute angle and tan , , + , cot , , = 2 , find t

Question

If $θ$ is an acute angle and $t an θ + co t θ = 2$ , find the value of $t a n^{7} θ + co t^{7} θ .$

Views: 726 students

Found 6 tutors discussing this question

Camila Discussed

θ

is an acute angle and

t an θ + co t θ = 2

, find the value of

t a n^{7} θ + co t^{7} θ .

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

t an θ + co t θ = 2

\Rightarrow t an θ + \frac{1}{t an θ}

= 2

\Rightarrow \frac{t a n ^{2} θ + 1}{t an θ}

= 2

\Rightarrow t a n^{2} θ - 2 t an θ

+ 1 = 0

\Rightarrow (t an θ - 1)^{2}

= 0

\Rightarrow t an θ - 1 = 0 \Rightarrow t an θ = 1 \Rightarrow t an θ = t an 4 5^{\circ} \Rightarrow θ = 45

∴ t a n^{7} θ + co t^{7} θ = t a n^{7} 4 5^{\circ} + co t^{7} 4 5^{\circ} = (t an 4 5^{\circ})^{7} + (co t 4 5^{\circ})^{7} = (1)^{7} + (1)^{7} = 2

Was this solution helpful?

150

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	If $θ$ is an acute angle and $t an θ + co t θ = 2$ , find the value of $t a n^{7} θ + co t^{7} θ .$
Answer Type	Text solution:1
Upvotes	150