Question

cot inverse 9 + cosec inverse root41/4 =pi/4​

Answer 1

Answer:

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Answer 2

let cot-¹(9) = A ⇒cotA = 9/1

then, sinA = 1/√(9² + 1²) = 1/√82

cosA = 9/√82

similar, cosec-¹(√41/4) = B ⇒cosecA = √41/4

then, sinB = 4/√41 ,

cosB = √(41 - 16)/√41 = 5/√41

now cot-¹(9) + cosec-¹(√41/4) = A + B

sin(cot-¹(9) + cosec-¹(√41/4)) = sin(A + B) = sinA.cosB + cosA.sinB

= 1/√82 × 5/√41 + 9/√82 × 4/√41

= 5/41√2 + 36/41√2

= (41)/41√2

= 1/√2 = sin(π/4)

⇒cot-¹(9) + cosec-¹(√41/4) = sin-¹(sin(π/4)) = π/4 [hence proved ]

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