Find the value of cos−1(2+34) I am trying to solve: sin−1cot⁡(cos−1(2+34)+cos−1(124)+csc−1(2)) My solution is as follow: T=sin−1cot⁡(cos−1(2+34)+cos−1(124)+csc−1(2)) Since: csc−12=sin−1(12)=π4; cos−1(124)=cos−1(32)=π6 Then: T=sin−1cot⁡(cos−1(2+34)+π4+π6) I am not able to proceed further.

Question

Find the value of cos−1(2+34)  I am trying to solve:  sin−1cot⁡(cos−1(2+34)+cos−1(124)+csc−1(2))  My solution is as follow:  T=sin−1cot⁡(cos−1(2+34)+cos−1(124)+csc−1(2))  Since:  csc−12=sin−1(12)=π4; cos−1(124)=cos−1(32)=π6  Then:  T=sin−1cot⁡(cos−1(2+34)+π4+π6)  I am not able to proceed further.

Vivian Soares · Accepted Answer

Hint:  y=y+34=(3+1)28  y=3+122=cos⁡π6cos⁡π4+sin⁡π6cos⁡π4=cos⁡(π4−π6)

Ella Williams · Accepted Answer

θ=cos−12+34  cos⁡θ=2+34   cos2θ=2+34   12+12cos⁡2θ=2+34   2+2cos⁡2θ=2+3   cos⁡2θ=32   2θ=π6   θ=π12

nick1337 · Accepted Answer

If α=cos−1⁡(2+34), then 4cos2⁡α=2+3 This means 3=4cos2⁡α−2=2(2cos2⁡α−1)=2cos⁡2α 2α=cos−1⁡32=π6. So α=π12 So T=sin−1⁡cot⁡(π2)=sin−1⁡0=0

Find the value of \cos^{-1}(\sqrt{\frac{2+\sqrt3}{4}}) I am trying to solve: \sin^{-1}\cot(\cos^{-1}(\sqrt{\frac{2+\sqrt 3}{4}})+\cos^{-1}(\frac{\sqrt{12}}{4})+\csc^{-1}(\sqrt2)) My

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