Question

sec theta minus tan theta equal to 5 and sec theta + tan theta equal to 1 by 5 then sin theta equal to​

Answer 1

Answer:

Sinθ = -12/13

Step-by-step explanation:

Given----> Secθ - tanθ = 5 and Secθ + tanθ = 1 / 5

To find-----> Value of Sinθ

Solution------> ATQ,

Secθ - tanθ = 5 .....................( 1 )

Secθ +tanθ = 1 / 5 ..................( 2 )

Adding equation ( 1 ) and ( 2 )

( Secθ - tanθ ) + ( Secθ + tanθ ) = 5 + ( 1 / 5 )

=> 2 Secθ = ( 25 + 1 ) / 5

=> 2 Secθ = 26 / 5

=> Secθ = 26 / ( 5 × 2 )

=> Secθ = 13 / 5

=> Cosθ = 1 / Secθ

=> Cosθ = 5 / 13

Now putting Secθ = 13 / 5 , in equation ( 1 )

( 13/5 ) - tanθ = 5

=> - tanθ = 5 - ( 13/5 )

=> - tanθ = ( 25 - 13 ) / 5

=> - tanθ = 12 / 5

=> tanθ = - ( 12 / 5 )

Now,

Sinθ = ( Sinθ / Cosθ ) Cosθ

= tanθ × ( 1 / Secθ )

= ( -12/5 ) × ( 5/13 )

= - 12 / 13