tan( sin⁻¹ (3/5) + cot⁻¹ (3/2) ) का मान ज्ञात कीजिए
Answers
Step-by-step explanation:
See the above attachment
Given : tan( sin⁻¹ (3/5) + cot⁻¹ (3/2) )
To find : मुख्य मान ज्ञात कीजिए
Solution:
tan( sin⁻¹ (3/5) + cot⁻¹ (3/2) )
a = sin⁻¹ (3/5)
=> sina = 3/5
cosa = √(1 - sin²a)
=> cosa = √(1 -(3/5)²
=> cos a = 4/5
sina/cosa = (3/5)/(4/5)
=> tana = 3/4
=> a = tan⁻¹ (3/4)
b = cot⁻¹ (3/2)
=> cotb = 3/2
=> tan b = 2/3
=> b = tan⁻¹ (2/3)
tan( sin⁻¹ (3/5) + cot⁻¹ (3/2) )
= tan( tan⁻¹ (3/4) + tan⁻¹ (2/3))
हमें ज्ञात है की Tan( x + y) = (Tanx + tany)/(1 - tannx tany )
= (3/4 + 2/3) /( 1 - (3/4)(2/3))
= (9 + 8)/(12 - 6)
= 17/6
tan( sin⁻¹ (3/5) + cot⁻¹ (3/2) ) मान = 17/6
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