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Question

Find the value  (tan(2212)×(2+1) 


 


Solution

 We want to find tan (22 12). we know (22 12) = 452. it is easy to guess that we will be using

 trigonometric ratios of 45 to find tan 2212 now we have to think of some formula which connects

tan 2212 and tan 45. 
We know tan2A = 2tanA1tan2A 
If A = 2212 in this equation, we will get a quadratic in tan 2212 
tan45 = 1 = 2tan22121tan22212
tan22212+2tan22121=0 

tan 22 12=2±4+42 

                     = 2±4+42 

                     = 2±222

                     = -1 ±± 2 

Tan2212 is +ve

tan2212=1+2=21

2+1)tan2212=(2+1)(21)=1

Key steps (1) 22 12=452

                 (2) Guessing the relation which has tan 22 12 and tan 45 .  

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