Math, asked by gaganSharma7897, 9 months ago

cos⁻¹ 1213 + sin⁻¹ 35 = sin⁻¹ 5665 सिद्ध कीजिए

Answers

Answered by amitnrw
0

Given   :  Cos⁻¹ 12/13 +sin⁻¹ 3/5 = sin⁻¹ 56/65

To find :   सिद्ध कीजिए

Solution:

Cos⁻¹ 12/13 +sin⁻¹ 3/5 = sin⁻¹ 56/65

माना x =  Cos⁻¹ 12/13

=>Cosx  =12/13

sin²x = (1 - cos²x)

=> sin²x = ( 1 - (12/13)²)

=> sin²xy = (5/13)²

=> sinx = 5/13

x = sin⁻¹(5/13)

माना  y = sin⁻¹ 3/5

=>Siny  = 3/5

cos²y = (1 - sin²y)

=> cos²y = ( 1 - (3/5)²)

=> cos²y = (4/5)²

=> cosy = 4/5

=> y = cos⁻¹(4/5)

Cos⁻¹ 12/13 +sin⁻¹ 3/5 = sin⁻¹ 56/65

दोनों तरफ Sin लेने पर

Sin (Cos⁻¹ 12/13 +sin⁻¹ 3/5)  =Sin (sin⁻¹ 56/65)

LHS =  Sin (Cos⁻¹ 12/13 +sin⁻¹ 3/5)

Sin(x + y)  = SinxCosy + CosxSiny

=  Sin(sin⁻¹(5/13))Cos(cos⁻¹ 4/5)+  Cos(Cos⁻¹ 12/13)Sin(sin⁻¹(3/5))

=  (5/13)(4/5)  + (12/13)(3/5)

= 20/65 + 36/65

= 56/65

RHS = Sin(Sin⁻¹ (33/65))

=56/65

LHS = RHS

=>Cos⁻¹ 12/13 +sin⁻¹ 3/5 = sin⁻¹ 56/65

QED

इति सिद्धम

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