2sin⁻¹35 = tan⁻¹ 247 सिद्ध कीजिए
Answers
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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