Question

please solve this question

Answer 1

Hi ,

Here I am using A instead of theta.

cot A = √3 ---( 1 )

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We know that ,

1 ) cosec² A = 1 + cot² A

2 ) sec² A = 1 + tan² A

3 ) tanA = 1/cot A

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( cosec² A + sec² A )/( cosec² A - sec² A )

= (1+cot² A+1+tan² A)/[1+cot² A-(1+tan² A)]

= ( 2 + cot² A + tan² A )/( 1+cot² A-1-tan²A )

= ( 2 + cot² A + tan² A )/ ( cot² A - tan² A )

= ( 2 + cot² A + 1/cot² A )/( cot² A - 1/cot² A )

= [ 2 + ( √3 )² + 1/( √3 )² ]/ [ ( √3 )² - 1/( √3 )² ]

= ( 2 + 3 + 1/3 ) / ( 3 - 1/3 )

= ( 5 + 1/3 )/ ( 3 - 1/3 )

= ( 15 + 1 )/( 9 - 1 )

= 16/8

= 2

I hope this helps you.

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