Question

If sin x= 12/13 and x lies in the second quadrant, show that sec x + tan x = -5

Answer 1

Go through the pic

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Answer 2

By the given explanation it is true that sec x + tan x = - 5

Given:

sin x= 12/13 and x lies in the second quadrant

To find:

Show that sec x + tan x = - 5

Solution:

Condition used:

From Trigonometric identites

=> sin²θ + cos²θ = 1  

=> cos θ = √[1 - sin²θ ]  

From Trigonometric ratios

=> tan = sin/cos

Given that

sin x = 12/13  

By the given condition

cos x = √[1 - (12/13)² ]  

= √[1 - (144/169) ]    

= √[(169 - 144)/169) ]     [ take 169 as Lcm ]

= √[(25)/169) ]  

= ± 5/13  

Given that 'x' lies in 2nd quadrant then cos θ will be negative

=> cos x = - 5/13    

=> sec x = - 13/5    [ ∵ sec = 1/cos ]

=> tan x = [ 12/13 ] / [-5/13]

=> tan x = -12/5

Substitute above values in given condition

=> sec x + tan x = -13/5 + (-12/5)

=> sec x + tan x = - 25/5

=> sec x + tan x = - 5

Hence,

It is proven that sec x + tan x = - 5

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