show that 1/cos(12/13)+1/sin(3/5)=1/sin(56/65)
Answers
Answer:
Step-by-step explanation:
⇒ cos¯¹ 12/13 + sin¯¹ 3/5 = sin¯¹ 56/65
Taking L.H.S. :
⇒ sin¯¹ 5/13 + sin¯¹ 3/5
Using the formula, sin¯¹x + sin¯¹y = sin¯¹ ( x√1-y² + y√1-x² )
⇒ sin¯¹ ( 5/13 √1-9/25 + 3 √1-25/169)
⇒ sin¯¹ ( 5/13 × 4/5 + 3/5 × 12/13)
⇒ sin¯¹ (30 + 36 / 65)
⇒ sin¯¹ (56/ 65)
Hence proved
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Similar questions ❤
Let x= cos-1(12/13)
Cosx =12/13
Sinx = root over 1-cos²x
=Root over 1-(12/13)²
=root over 1-144/169
=root over 25/169
Sinx=5/13
Again let y= sin -¹3/5
Sin y=3/5
Cos y=root over 1-sin²y
=root over 1-(3/5)²
=root over 1-9/25
=root over 16/25
Cos y = 4/5
Sin (x+y)= sinxcosy + cosxsiny
Sin(x+y)= 5/13×4/5+12/13×3/5
20/65 + 36/65
56/65
Sin(x+y) = 56/65
x+y= sin-¹ 56/65
cos-¹(12/13) + sin-¹(3/5) = sin-¹(56/65)
Answer:
Step-by-step explanation:
