Question

If 4x=cosec A and 4/x = cotA, find the value of 4[x²-1/x²]
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

Solution:

Given:
4x= cosecA
x= cosecA/4

And  4/x = cotA
1/x= cotA/4

4[x²-1/x²]= 4[(cosecA/4)² - (cotA/4)²]

(PUTTING THE VALUES OF X AND 1/X)

4[x²-1/x²]= 4[ cosec²A/16 - cot²A/16]

4[x²-1/x²]= 4[(cosec²A- cot²A)/16]
4[x²-1/x²]= 4[1/16]       (cosec²A- cot²A=1)
4[x²-1/x²]= 4/16= ¼
4[x²-1/x²]=¼

HOPE THIS WILL HELP YOU....

Answer 2

Hi 

4x = cosec A 

x = cosec A /4 

x² = cosec² A /16 ____(1)

4/x = cot A 

1/x = cot A/4

1/x² = cot² A /16  _____(2)

4( x² - 1/x² ) 

4( cosec² A /16  - cot² A /16 ) 

4 ( cosec²A - cot²A /16) 

 ( 1/sin² A - cos²A/sin² A)/4

(1 - cos²A)/sin²A /4

sin²A / sin²A /4 

1/4