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Refer to the triangle given in figure. Find: | ^{2}C, - , {1}{

Question

Refer to the triangle given in figure.
Find: $∣ ∣ cot^{2} C - \frac{1}{sin ^{2} C} ∣ ∣$

A

1

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Refer to the triangle given in figure.
Find:

∣ ∣ cot^{2} C - \frac{1}{sin ^{2} C} ∣ ∣

12 mins ago

Discuss this question LIVE

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Text solutionVerified

Given,

△ A BC

, A perpendicular from B on AC, let it cut AC at D, such that

∠ B D A = ∠ B D C = 9 0^{\circ}

A D = 3

,

B D = 4

and

BC = 12

In

△ A B D

,

A B^{2} = B D^{2} + A D^{2}

A B^{2} = 3^{2} + 4^{2}

A B = 5

In

△ BC D

B C^{2} = C D^{2} + B D^{2}

1 2^{2} = C D^{2} + 4^{2}

C D^{2} = 128

C D = 82

Now,

∣ ∣ cot^{2} C - \frac{1}{sin ^{2} C} ∣ ∣ = ∣ ∣ cot^{2} C - csc^{2} C ∣ ∣ = ∣ ∣ (\frac{B}{P})^{2} - (\frac{H}{P})^{2} ∣ ∣

=

∣ ∣ (\frac{8 2}{4})^{2} - (\frac{12}{4})^{2} ∣ ∣

=

∣8 - 9∣

=

1

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Question Text	Refer to the triangle given in figure. Find: $∣ ∣ cot^{2} C - \frac{1}{sin ^{2} C} ∣ ∣$
Answer Type	Text solution:1
Upvotes	150