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Find the value of Tan 15 + cot 75 ? How can we solve it

Find the value of Tan 15 + cot 75 ? How can we solve it 

Grade:11

2 Answers

Shahid
74 Points
7 years ago
To Find : the value of Tan15 + Cot15 
 
Solution: 
tan15 + cot15 
= tan15 + (1/tan15)
= (tan215 + 1) / tan15
= sec215 / tan15                                                         {As Sec2x-tan2x = 1}
= (1/cos215) / (sin15/cos15)                                        
= 1 /( sin15 x cos15)
= 2 / sin30                                                         {As 2sinxcosx = sin2x}
= 2 /(1/2) 
=4
Amreen
45 Points
7 years ago
to find tan 15+cot 75
tan 15+ cot(90-15)   // cot(90-x) is tan x
so, tan 15+tan 15=2tan 15
2tan(45-30)=2.(tan 45-tan 30)/(1+tan 45.tan 30)
substitute the values for each and finally you get 4-2.3^1/2
=0.535

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