Question

Answer the question

Answer 1

Hey buddy B-)

here,
cosec A + cot A = 3/2 -(given) - - - eq 1

now we know that,

=> cosec²A - cot²A = 1

now, using ( a^2 - b^2 )formula,

=> (cosec A + cot A)(cosec A - cot A) = 1

=> 3/2(cosec A - cot A)= 1

=> (cosec A - cot A) = 2/3 - - - - eq 2

now, subtracting eq 2 from eq 1.... We get, 1

=> 2cosec A = 13/6

=> cosec A = 13/12

so, sin A = 12/13

now, we know that

=> sin^2 A + cos^2 A = 1

so,

=> cos A = (1 - sin^2 A) ^1/2

(: - sin^2 A = 144/169)

=> cos A = (25/169) ^1/2

=> cos A = 5/13

: -) ' hence proved '

(edit : I'm using A instead of theta)

HOPE THIS HELPS YOU (^o^)