Question

evaluate
sin [2cot-1 1/5]

Answer 1

Answer:

|| ❀ᴀɴsᴡᴇʀ❀ ||

➺ sin (2cot -1 (-5/12)

=> cot -1 (-5/12) = y

=> cot y = -5/12 = B/P (B = base, P = perpendicular)

➺ (means it is in 2nd Quadrant)

➺ In second Quadrant sin θ is +ve

while cos θ is -ve

(H² = 12² + 5² (Pythagorean theorem)

=> H = 13)

➺ cot y = -5/12 so, sin y = 12/13

cos y = -5/13

➺ sin 2 y = 2 sin y cos y

=> 2 × 12/13 × -5/13

=> -120/169

|| ☬☨ᴍɪss_ɪɴɴᴏᴄᴇɴᴛ☨☬ ||

Answer 2

Answer:

-120/169

Step-by-step explanation:

Given:

Sin[2 * $Cot^{-1} (\frac{1}{5})$]

To find:

The value of Sin[2 * $Cot^{-1} (\frac{1}{5})$]

Solution:

Firstly we evaluate the $Cot^{-1}(\frac{1}{5} )$

=> cot -1 (-5/12) = y

=> cot y = -5/12 = B/P (B = base, P = perpendicular)

(means it is in 2nd Quadrant)

In second Quadrant sin θ is +ve, while cos θ is -ve

H² = 12² + 5² (Pythagorean theorem)

=> H = 13

cot y = -5/12 so, sin y = 12/13

cos y = -5/13

sin 2 y = 2 sin y cos y

=> 2 × 12/13 × -5/13

=> -120/169

Hence, the value of Sin[2 * $Cot^{-1} (\frac{1}{5})$] = -120/169.

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