Question

sec^2 129 - cosec^2 31/ cosec 39 - sec 121​

Answer 1

Given :  (Sec² 129  - Cosec² 31 ) / ( Cosec 39 - Sec 121)  

To Find : Simplify

Solution:

(Sec² 129  - Cosec² 31 ) / ( Cosec 39 - Sec 121)

Sec (90 + α )  = - Cosecα

=> Sec ( 129 ) = Sec ( 90 + 39)  = - Cosec 39

=> Sec ( 121 ) = Sec ( 90 + 31)  = - Cosec 31

= ((-Cosec39)²   - Cosec² 31 ) / ( Cosec 39 -  (-Cosec 31))

= (Cosec² 39 - Cosec²31 ) / ( Cosec 39 + Cosec 31)

= ( Cosec 39 + Cosec 31) (Cosec 39 - Cosec 31 ) /  ( Cosec 39 + Cosec 31)

=  Cosec 39 - Cosec 31

(Sec² 129  - Cosec² 31 ) / ( Cosec 39 - Sec 121)  =  (Cosec 39 - Cosec 31 )

Learn More:

sin(-1845),cos(2190)tan(3645)sec(480)cosec(870)

https://brainly.in/question/11672495

70. prove that(cos A cosec A - sin A sec A)/cos A + sin A= cosec A ...

https://brainly.in/question/11611272