Question

Show that sin⁻¹ 12/13 + cos⁻¹ 4/5 + tan⁻¹ 63/16 = π

Answer 1

https://youtu.be/0j7XMpxddqU

This will help you.
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Answer 2

Answer:

Step-by-step explanation:

sin⁻¹ 12/13 + cos⁻¹ 4/5 + tan⁻¹ 63/16 = π

=>sin⁻¹ 12/13 + cos⁻¹ 4/5 =  π - tan⁻¹ 63/16

=> Sin(sin⁻¹ 12/13 + cos⁻¹ 4/5) = Sin( π - tan⁻¹ 63/16)

=> Sin(sin⁻¹ 12/13)Cos(cos⁻¹ 4/5) + Cos(sin⁻¹ 12/13)(Sincos⁻¹ 4/5) = Sin(tan⁻¹ 63/16)

sin⁻¹ 12/13 = Cos⁻¹5/13    & cos⁻¹ 4/5 = Sin⁻¹ 3/5

=> 12/13 * 4/5  + 5/13 * 3/5 = Sin(tan⁻¹ 63/16)

=> 48/65  + 15/65 = Sin(tan⁻¹ 63/16)

=> 63/65 = Sin(tan⁻¹ 63/16)

=>Sin⁻¹(63/65) = tan⁻¹ 63/16

Sin⁻¹(63/65) = Cos⁻¹(16/65)

Sin⁻¹(63/65) /Cos⁻¹(16/65) = Tan⁻¹ (63/16)

=> Tan⁻¹ (63/16) = tan⁻¹ 63/16

QED