Question

If the angles of ∆ABC are in ratio 1:1:2, respectively (the largest angle being angle C), then the value of secA/ cosec B – tanA /cot B is​

Answer 1

Answer:

Answer is 0

Step-by-step explanation:

Make a triangle ABC with angle C=90

Consider secA/cosecB

This will be equal to AB/AC x AC/AB=1

Consider tanA/cotB

This will be equal to BC/AC x AC/BC=1

Hence, 1-1=0

Answer 2

Given : If the angles of ∆ABC are in ratio 1:1:2, respectively (the largest angle being angle C),

To find : the value of secA/ cosec B – tanA /cot B  

Solution:

angles of ∆ABC are in ratio 1:1:2,

Let say angles are  x , x , 2x

Sum of angles of a triangle = 180°

=> x + x + 2x = 180°

=> 4x = 180°

=> x = 45°

=> 2x = 90°

A = B = 45°   and C =  90°  as C  being largest

secA/ cosec B – tanA /cot B

SecA  = Sec 45° = √2

Cosec B = Cosec 45° = √2

tanA = tan 45° = 1

Cot B = cot 45° = 1

= √2 / √2   -  1/1

= 1  -  1

= 0

secA/ cosec B – tanA /cot B   = 0

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