Math, asked by mahekmughal6995, 10 months ago

2sin⁻¹35 = tan⁻¹ 247 सिद्ध कीजिए

Answers

Answered by amitnrw
0

Given   :  2sin⁻¹(3/5) = tan⁻¹ (24/7)

To find :   सिद्ध कीजिए

Solution:

2sin⁻¹(3/5) = tan⁻¹ (24/7)

माना  x = sin⁻¹(3/5)

=> sinx = 3/5

Cos²x = (1 - sin²x)

=> cos²x = ( 1 - (3/5)²)

=> cos²x = (4/5)²

=> cosx = 4/5

sinx/Cosx  = (3/5)/(4/5)

=> tanx = 3/4

=> x = tan⁻¹ (3/4)

2 tan⁻¹ (3/4) =  tan⁻¹ (24/7)

दोनों तरफ  tan लेने पर

tan (2 tan⁻¹ (3/4)) =  tan( tan⁻¹ (24/7))

LHS =  tan (2 tan⁻¹ (3/4))

tan2x = 2tanx /(1 - tan²x)

=  2(3/4) /( 1 - (3/4)²)

= (3/2)/(( 16 - 9)/16)

= 3 * 16 /   2 * 7

= 24/7

RHS = 24/7

LHS = RHS

=> 2sin⁻¹35 = tan⁻¹ 247

QED

इति सिद्धम

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