Question

If 5secθ- 12cosecθ=0, find the values of secθ, cosθ and sinθ.

Answer 1

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Answer 2

Solution :

Here I am using A instead of theta.

i )Given 5secA - 12cosecA = 0

=> 5secA = 12cosecA

=> 5/cosA = 12/sinA

=> ( SinA/cosA ) = 12/5

=> tan A = 12/5

ii ) sec² A = 1 + tan²A

= 1 + ( 12/5 )²

= 1 + 144/25

= ( 25 + 144 )/25

= 169/25

Sec A = √ 169/25

SecA = 13/5

iii ) cos A = 1/secA

= 1/( 13/5 )

= 5/13

iv ) sinA = tan A × cosA

= ( 12/5 ) × ( 5/13 )

= 12/13

Therefore ,

Sec A = 13/5 ,

Cos A = 5/13

SinA = 12/13

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