Question

If cosec a = 2,
find
1 ÷ tan a + sin a ÷1 + cos a​

Answer 1

Step-by-step explanation:

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