If tan A = 1 / √10 and A is an acute angle, find the value of sin A + cosec A.

Question

Accepted Answer

Given tan A = 1 / √10 and A is acute.

Step 1: Recall that tan A = opposite / adjacent.  
Let opposite side = 1, adjacent side = √10.

Step 2: Calculate hypotenuse using Pythagoras theorem:  
Hypotenuse = √(1^2 + (√10)^2) = √(1 + 10) = √11.

Step 3: Calculate sin A:   
sin A = opposite / hypotenuse = 1 / √11.

Step 4: Calculate cosec A:   
cosec A = 1 / sin A = √11 / 1 = √11.

Step 5: Calculate sin A + cosec A:  
= (1 / √11) + √11 = (1 + 11) / √11 = 12 / √11.

Step 6: Check options:  
12 / √11 is option 3.

Therefore, the correct answer is 12 / √11.

Answer

Answer

Answer