Question

Prove that tan 315 degree cot(-405)degrees+cot 495 degrees tan(-585)=2

Answer 1

please see the attachment

Answer 2

Answer:

2

Step-by-step explanation:

We have been given

tan 315 degrees * cot( -405 ) degree + cot 495 degrees* tan(-585) degree

= 2

We are solving at left hand side

tan 315 degrees * cot( -405 ) degree + cot 495 degrees* tan(-585) degree

= tan ( 360° - 15° ) * tan ( 360° + 45° ) + cot ( 360° +135° ) *tan (360° + 225° )

= ( - tan 45° ) * ( - tan 45° ) + cot ( 180° - 45°  )* (tan 180° + 45° )

= tan 45° * tan 45° + cot 45° tan 45°

= 1 * 1 + 1 * 1

=1 + 1

2

Now

Prove that  

tan 315 degrees * cot( -405 ) degree + cot 495 degrees* tan(-585) degree

= 2