8.2 1(iv)

(iv) (sin30⁰ + tan45⁰ – cosec60⁰) / (sec30⁰ + cos60⁰ + cot45⁰)

हल –

(sin30⁰ + tan45⁰ – cosec60⁰) / (sec30⁰ + cos60⁰ + cot45⁰)

= ( 1/2 + 1 – 2/√3 ) / ( 2/√3 + 1/2 + 1 )

= (3/2 – 2/√3) / ( 2/√3 + 3/2 )

= (3√3 – 4)/2√3 / (4 + 3√3)/2√3

= (3√3 – 4) / 2√3  x  2√3 / (4 + 3√3)

= (3√3 – 4) / (4 + 3√3)

हर का परिमेयकरण करने पर

= (3√3 – 4) / (4 + 3√3)  x = (4 - 3√3) / (4 - 3√3)

= (3√3 – 4)(4 - 3√3) / (4 + 3√3) (4 - 3√3)

= (12√3 – 16 - 27 + 12√3) / (4)² - (3√3)² 

= (24√3 – 43) / (16 – 27) 

= (24√3 – 43) / (-11) 

= -(-24√3 + 43) / (-11) 

= (-24√3 + 43) / 11 

= (43 - 24√3 ) / 11