1. If cosec a- cot a= 1/2,0< a <π/2, then what is the value of cos a?
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Answer:
cosecA =2
=> sinA = 1/2 ……….(1)
So, cosA = √(1-sin²A)
=> √(1 - 1/4)
=>√(3/4)
=> √3/2 ………….(2)
So, tanA = 1/2 / √3/2
= (1/2) * (2/√3)
= 1/√3 …………(3)
Now in 1/tanA + sinA/(1+cosA)
By (1), (2) & (3), put the values…
= 1/(1/√3) + (1/2) / ( 1+ √3/2)
= √3 + (1/2) / {(2+√3)/2}
= √3 + 1/(2+√3)
= (2√3 + 3 + 1) / (2+√3)
= 2( √3+2) / (√3+2)
= 2
Step-by-step explanation:
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