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

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

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Elijah 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 .

11 mins ago

Discuss this question LIVE

11 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

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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